Modified from Irving L. Jensen's excellent work "Jensen's Survey of the NT"

AND DO NOT BE CONFORMED: me sunschematizesthe (2PPPM) (Ex 23:2; Lev 18:29,30; Dt 18:9-14; Jn 7:7; 14:30; 15:19; 17:14; 1Co 3:19; 2Co 4:4; 6:14-17; Gal 1:4; Eph 2:2; 4:17-20; Js 1:27; 4:4; 1Pe 1:14,18; 4:2; 2Pe 1:4; 2:20; 1Jn 2:15-17; 3:13; 4:4,5; 5:19; Rev 12:9; 13:8)

Don’t let the world around you squeeze you into its own mold. (Phillips )
And do not fashion yourselves after this world (EMTV)
Stop being molded by the external and fleeting fashions of this age but

Wuest has an enlightening expanded rendering...

And stop assuming an outward expression that does not come from within you and is not representative of what you are in your inner being but is patterned after this age; but change your outward expression to one that comes from within and is representative of your inner being, by the renewing of your mind, resulting in your putting to the test what is the will of God, the good and well-pleasing and complete will, and having found that it meets specifications, place your approval upon it. (Wuest, K. S. Wuest's Word Studies from the Greek New Testament: Eerdmans or Logos)

Do not be conformed is a negative particle (Greek = me) plus the present imperative which conveys the sense of "Stop doing this!" implying that they were already allowing themselves to be poured into the mold of the godless, even anti-God world.  Paul commands them to stop acting like earth dwellers. However do not misunderstand what he is saying. He is not saying believers are to make a list of "don't's" which we need to stop doing -- that is the essence of legalism (listen to Pastor Ray Stedman's excellent Mp3  entitled Legalism) (Transcipt)

Frederick Godet explains it this way...

Paul has just pointed to the believer's body as a consecrated instrument...In the use of his consecrated body, the believer has first an everywhere present model to be rejected, then a new type to be discerned and realized. The model to be rejected is that presented to him by the present world , or, as we should say, the reigning fashion , taking this word in its widest sense...The term (this) present world is used in the Rabbins to denote the whole state of things which precedes the epoch of the Messiah; in the N. T. it describes the course of life followed by those who have not yet undergone the renewing wrought by Christ in human life. It is this mode of living anterior to regeneration which the believer is not to imitate in the use which he makes of his body. (Godet, F. L.: The Epistle of St Paul to the Romans) (Bolding added)

Conformed (4964) (suschematizo from sun = together with + schêma = external form, appearance) means to form according to a pattern or mold,  to fashion alike, to conform to the same pattern outwardly. The meaning is to form or mold one’s behavior in accordance with a particular pattern or set of standards. The preposition "sun" in this compound verb denotes a personal assimilation to or conformity with the pattern indicated.

Suschematizo is used only here and in 1 Peter 1:14 (see notes) where it describes those who conform themselves to their former lusts (strong desires in this context that emanate from the fallen nature, the flesh, that evil disposition inherited from Adam) which were theirs in their ignorance (before God in His kindness opened the eyes of their heart to see the liberating truth of the Gospel and the new life in Christ Jesus their Lord). (Click in depth analysis of suschematizo)

To reiterate, suschematizo refers to an outward expression that does not reflect (or come from) what is within, in this case Christ in us the hope of glory (see note Colossians 1:27), Christ our life (see note Colossians 3:4). Suschematizo is used of masquerading or putting on an act, specifically by following a prescribed pattern or scheme (a "schema"). The root noun schema (also source of English word scheme = a systematic plan or arrangement for attaining some particular object or putting a particular idea into effect) denotes a pattern of life that does not come from within but is imposed from without, in this case this present evil age (Gal 1:4) or world system which lies in the power of the evil one (1John 5:19).

Suschematizo also conveys the thought of following a manner of life that is unstable and changing rather than enduring. Paul’s prohibition is directed against a manner of life that does not come from nor is representative of the new creatures (creations) believers are in their inner being as the result of regeneration by the Holy Spirit Who now indwells every child of God (see note Romans 8:9).
           
William Barclay explains that the root of suschematizo:

is schema, which means the outward form that varies from year to year and from day to day. A man’s schema is not the same when he is seventeen as it is when he is seventy; it is not the same when he goes out to work as when he is dressed for dinner. It is continuously altering. So Paul says, “Don’t try to match your life to all the fashions of this world; don’t be like a chameleon which takes its colour from its surroundings. (Barclay, W: The Daily Study Bible Series. The Westminster Press or Logos)

Not being conformed is not a negative approach so much as it is a positive one. It is not that you stop doing a few things that other people are doing that are regarded as "wrong". It is more that you start doing some things that they don't do at all, like loving your enemy (try this one in your own strength), forgiving when you have been unjustly wronged, returning good for evil,  showing kindness to those who are repay you with an ungrateful attitude. These are attitudes and actions that living sacrifices are to carry out. This quality of conduct is what it looks like practically to not be conformed to the world. The way to see this supernatural lifestyle become a reality is to "be transformed by having your mind renewed" so that you begin to think less and less like the fallen world thinks and more and more like Christ in us would have us think and act. 

Dear Christian, how is your love for Christ today
compared to your love when you first met Him by grace through faith?

C H Spurgeon in his highly recommended devotional (Morning and Evening) addresses this question expounding on the inestimable worth of not being conformed to the world...

If a Christian can by possibility be saved while he conforms to this world, at any rate it must be so as by fire (cp Jude 1:23). Such a bare salvation is almost as much to be dreaded as desired. Reader, would you wish to leave this world in the darkness of a desponding death bed, and enter heaven as a shipwrecked mariner climbs the rocks of his native country? Then be worldly; be mixed up with Mammonites (those devoted to the pursuit of wealth), and refuse to go without (outside) the camp bearing Christ's reproach (see note Hebrews 13:13).

But would you have a heaven below as well as a heaven above? Would you comprehend with all saints what are the heights and depths, and know the love of Christ which passeth knowledge? (see notes Ephesians 3:18; 3:19) Would you receive an abundant entrance into the joy of your Lord? (see notes 2Peter 1:10-11) Then come ye out from among them, and be ye separate, and touch not the unclean thing (2Cor 6:17, Isaiah 52:11). Would you attain the full assurance of faith (see note Hebrews 10:22)? You cannot gain it while you commune with sinners.

Would you flame with vehement (marked by intensity of feeling or conviction) love? Your love will be damped (literally made slightly wet but here figuratively meaning stifled or deadened!) by the drenchings of godless society. You cannot become a great Christian - you may be a babe in grace, but you never can be a perfect man in Christ Jesus while you yield yourself to the worldly maxims (short, pithy statements expressing general truths or rules of conduct) and modes of business of men of the world.

It is ill for an heir of heaven to be a great friend with the heirs of hell (read especially James 4:4)

It has a bad look when a courtier (a companion to a king, in our case the King of kings!) is too intimate with his king's enemies.

Even small inconsistencies are dangerous. Little thorns make great blisters, little moths destroy fine garments, and little frivolities (those things not having any serious purpose or value) and little rogueries (dishonest, unprincipled,  mischievous ways of conduct - in agriculture a rogue is a crop plant which is inferior, diseased, or of a different, unwanted variety!) will rob religion of a thousand joys.

O professor (a person who affirms a faith in or allegiance to something), too little separated from sinners, you know not what you lose by your conformity to the world. It cuts the tendons of your strength, and makes you creep where you ought to run. Then, for your own comfort's sake, and for the sake of your growth in grace (see note 2 Peter 3:18), if you be a Christian, be a Christian, and be a marked and distinct one. (Amen!) (Ed note: Bolding, definitions and Scriptural references added for amplification and emphasis).

Do you understand what Spurgeon is saying? If the passion and flame we once had for Christ has lessened, one of the reasons may be that we have become too enamored with this present evil age. Nothing will dampen our love for Christ as will love for the world. (cp notes on "two masters" in Matthew 6:24)

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Romans 12:1 (note) speaks of a specific act in which we offer ourselves to God and Romans12:2 tells us of two ongoing activities (both are present tense) that carry out the intent to present ourselves as a living sacrifice.
      
A believer’s continued practice of conforming to the world's way of thinking and acting is inconsistent with having given his or her body to the Lord the King and to the King's service. Indeed, such a practice is forbidden because it negates and seriously mars the presentation the believer has made as a living sacrifice and amounts in essence to a  sacrifice that places itself on the altar but then begins to "crawl off the altar". To reiterate the present tense of the verb suschematizo indicates that this duty to resist conformity is necessary every moment of every day for the rest of our life on earth. Whereas Romans 12:1 (see notes) calls for a decisive commitment, (Romans 12:2) deals with the maintenance of that commitment. The process of non-conformity is a continuous duty that runs parallel with the continual process of being transformed (see discussion below) or as Harris summarizes it -- "a continual renunciation and renewal."

We are to stop allowing ourselves to be fashioned after the schemes of this passing evil age in which we live. Practically this means we must be careful what we read and watch (see discussion of to this world below). We must not be afraid to be different (to be like Christ - see John 15:18-21).  This same idea of not being conformed to the world is found in  2 Timothy 2:4,

No soldier engaged in active duty entangles himself with the everyday affairs of this life. (see note on 2 Timothy 2:4)

You can’t be in God's army and be a civilian. You can't serve God and mammon (see note Matthew 6:24). As citizens of heaven (see note Philippians 3:20) we are to “set [our] mind on things above, not on the things that are on the earth" (see notes Colossians 3:1; 3:2).             
           
The danger of being conformed to the world's way of thinking and doing is ever present. James says that those who seek to practice pure and undefiled religion must keep themselves unstained by the world (Ja 1:27). James further warns us of the danger of "Friendship of the world” (Ja 4:4).

Righteous Lot (see notes 2 Peter 2:7; 2:8; 2:9) represents a tragic OT example of a believer who gradually conformed to the world (and it cost him a "lot"). First he pitched his tent toward Sodom (Ge 13:10-11). Then he moved into Sodom (Ge 13:12,19:1). Before long, Sodom moved into him (conformed to the world) and he lost his testimony to the pagans and even with his own family (Ge 19:9,14, 26,1Co 15:33). When judgment fell on Sodom, Lot lost everything. Abraham, the separated believer, the friend of God (Js 2:23), had the greater ministry to the pagans than did Lot, the friend of the world.

Compromise
leads to
Conformity
which leads to
Defeat

It is when the believer is separated from sin (2Cor 6:14-7:1) that he or she exerts the greatest influence for God. The price of spiritual power is a purity of heart. As discussed below spiritual transformation starts in the mind and heart. A mind dedicated to the world and its concerns will produce a life tossed back and forth by the currents of culture (see note Ephesians 4:14). But a mind dedicated to God’s truth will produce a life that can stand the test of time. We can resist the temptations of our culture by meditating on God’s truth and letting the Holy Spirit guide and shape our thoughts and behaviors.

Expositor's Bible Commentary adds that

The dedicated life is also the transformed life. Whereas v1 has called for a decisive commitment, v2 deals with the maintenance of that commitment. We need to "bind the sacrifice with cords...unto the horns of the altar" (Ps 118:27). Significantly, there is a shift in the tense of the verbs (from the aorist "present") to the present tense, pointing up the necessity of continual vigilance lest the original decision be vitiated or weakened. The threat comes from "this world," whose ways and thoughts can so easily impinge on the child of God.  (Gaebelein, F, Editor: Expositor's Bible Commentary 6-Volume New Testament. Zondervan Publishing)

TO THIS WORLD (AGE): to aioni touto:

World (1658) (aion) (Click word study of aion) is better rendered as the age referring to the present sinful age which John reminds us "lies in the power of the evil one" (1Jn 5:19), Satan himself, who Paul describes as “the god of this world (aion)" (2 Cor 4:4). This present evil age is contrasted with the age to come (Mt 12:32).

William MacDonald explains that the world as...

as used here means the society or system that man has built in order to make himself happy without God. It is a kingdom that is antagonistic to God. The god and prince of this world is Satan (2Cor 4:4; John 12:31; 14:30; 16:11. All unconverted people are his subjects. He seeks to attract and hold people through the lust of the eyes, the lust of the flesh, and the pride of life (1John 2:16). The world has its own politics, art, music, religion, amusements, thought-patterns, and lifestyles, and it seeks to get everyone to conform to its culture and customs. It hates nonconformists—like Christ and His followers. Christ died to deliver us from this world. The world is crucified to us, and we are crucified to the world. It would be absolute disloyalty to the Lord for believers to love the world. Anyone who loves the world is an enemy of God. Believers are not of the world any more than Christ is of the world. However, they are sent into the world to testify that its works are evil and that salvation is available to all who put their faith in the Lord Jesus Christ." (MacDonald, W and Farstad, A. Believer's Bible Commentary: Thomas Nelson or Logos)

Trench has described aion as

that floating mass of thoughts, opinions, maxims, speculations, hopes, impulses, aims, aspirations, at any time current in the world, which it may be impossible to seize and accurately define, but which constitute a most real and effective power, being the moral, or immoral atmosphere which at every moment of our lives we inhale, again inevitably to exhale. 

Aion then is the spirit of this age that seeks gratification of self independent of and regardless of the consequences or cost to self or others. This "world" or age is self-centered, self-pleasing, self-indulgent, self-concerned and indifferent to needs of others. The prevailing, popular thinking and culture is in continual rebellion against God and His authority and seeks to conform all the world's inhabitants into its godless "world view". The "world's view" impregnates mankind, molding, corrupting and degrading and in the process affecting all culture and every institution.

This world or age is like that in the days of Judges when

there was no king in Israel; every man did what was right in his own eyes. (see notes Judges 17:6 Judges 21:25).

The result of being conformed to this age is not a renewed mind but

a depraved mind  (reprobate - a mind not enduring trial and so not of standard purity or fineness and in the final analysis a mind that is rejected) (which does) those things which are not proper, being filled with all unrighteousness, wickedness, greed, evil; full of envy, murder, strife, deceit, malice; they are gossips, slanderers, haters of God, insolent, arrogant, boastful, inventors of evil, disobedient to parents, without understanding, untrustworthy, unloving, unmerciful; and, although they know the ordinance of God, that those who practice such things are worthy of death, they not only do the same, but also give hearty approval to those who practice them." (see notes Romans 1:28; 29; 30; 31; 32).

This age contrasts sharply with "the age" (the messianic age or millennial reign of Christ on earth is the next "age")  to come when righteousness reigns (see note 2 Peter 3:13).

Paul writes that our Lord...

gave Himself for our sins so that He might rescue (to pluck out, tear out; take out from a number and so deliver, set free from danger) us from this present evil (pernicious) age (aion), according to the will of our God and Father (Gal 1:4).

Before we were saved, we were conformed to this present evil age and

walked ( ordered your behavior) according to (dominated by) the course  (aion - the spirit of the age) of this world (kosmos = world’s values and way of doing things), according to the prince of the power of the air" (see note Ephesians 2:2).

When we come to the kingdom of God, we should abandon the thought-patterns and lifestyles of the world because the world wants to control our mind, but God wants to transform our mind (cf notes Ephesians 4:17; 18; 19; 20; 21; 22; 23 24; Colossians 3:1ff).

And so because of the mercies of God, believers are in the world but are not to be of the world. This truth is illustrated by a submarine which is fully functional in water but is ruined if water comes within. A submarine on the ground (out of the water) is useless and is not accomplishing its mission. When it is in the water it must be insulated (not isolated) from the water. If the water ever gets into the submarine then there is cause to sound the alarm. Believers are to be insulated from the world (like Daniel in the midst of idol infested Babylon) but not isolated from the world.

A boat in the water is by design
but
Water in the boat is big disaster

Morris writes that...

 Christians have been introduced to the life o