If you have been raised in church you know this verse. It's a favorite of many Christ followers. Let's read it in a few different versions.
Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is —his good, pleasing and perfect will. (Romans 12:2 NIV).
Don’t copy the behavior and customs of this world, but let God transform you into a new person by changing the way you think. Then you will learn to know God’s will for you, which is good and pleasing and perfect. (NLT)
Don't become so well-adjusted to your culture that you fit into it without even thinking. Instead, fix your attention on God. You'll be changed from the inside out. Readily recognize what he wants from you, and quickly respond to it. Unlike the culture around you, always dragging you down to its level of immaturity, God brings the best out of you, develops well-formed maturity in you. (The Message)

I like the way The Message translation - don't become so well-adjusted to your culture...How should Christ-followers respond to their culture?  About a half century ago, H. Richard Niebuhr attempted to answer that question in his book Christ and Culture. He offered five possible responses to the question.
First, he said that some Christians have claimed that we should see our response as, “Christ against Culture.” In this view the Christian’s allegiance is only to Christ, and a radical choice confronts every person: either to follow Christ or the world. The prince of the world is the devil, therefore Christians should separate themselves and withdraw from the present evil culture and condemn it.
The second response he calls "Christ of Culture".  These would be cultural Christians who say that the Gospel should be interpreted according to current intellectual and scientific categories. They embrace the culture and believe it is necessary for Christians to accommodate to it. Whereas the first group would separate itself from the culture, this group would blend into it. 
The third response is “Christ above Culture.” Niebuhr calls the people in this group synthesists because they want to bring together the values of Christ and the culture. They claim that there are other laws besides the laws of Jesus Christ; and it is necessary to follow them. Christians live in the material world, but seek to rise above the material world by following the ideals taught by Christ. 
The fourth response is “Christ and Culture in Paradox.” The paradox view says that both Christ and the culture claim our loyalty, and we live in that tension which is never resolved in this life. The culture may force us to do things against our conscience. Nevertheless, we have to live in the kingdom of God and the kingdom of this world, and we must live with the conflicts it causes. 
The fifth response is the correct one. He calls it "Christ the Transformer of Culture."  This view is optimistic about the ability of Christians to affect the culture. It believes that the culture cannot only be influenced, it can be converted. This was John Wesley’s view. It sees the church as called to be a holy community here on earth which serves as a testimony and model of what the world could be. The church is visibly set apart from the non-Christian culture, and yet it engages and serves it. The church does not change the world by its own effort, but it sees God at work as it remains faithful and continues to announce the good news. The church sees its responsibility to be Christ to the world. It does not believe that you can legislate Christianity into existence, but it sees God at work behind the scenes bringing about his kingdom — in spite of the resistance and even the hostility of the culture. 
So, don't be conformed to this world but be transformed by the renewing of your mind. God not only changes us; He can change our culture!