There is an interesting review by Andy Crouch of James D. Hunter's book, "To Change the World".
http://www.booksandculture.com/
Hunter, he writes, does not believe we should (or can) change the world. Nor should we be 'redeeming the culture,' 'advancing the kingdom,' 'building the kingdom,' 'transforming the world,' 'reclaiming the culture,' [or] 'reforming the culture.' According to Hunter, the strategies Christians have pursued are, by themselves, woefully incapable of changing the world. The premise is that once the hearts and minds of ordinary people are properly revived and informed, the culture will change. "This account," Hunter says flatly, "is almost wholly mistaken."
"It is mistaken", Crouch summarizes, "because of its individualism: it ignores the central role of institutions in transmitting culture. It is mistaken because it is not just institutions that matter, but institutions at the cultural "center" rather than the "periphery". It is mistaken, perhaps most of all, in its egalitarian assumption that the hearts and minds of ordinary people matter—in fact, cultural change is almost always driven by change among a small élite who occupy powerful positions in those culturally central institutions".
There are books such as "Under the Influence, How Christianity Transformed Civilization" by Alvin Schmidt, which document evidence to the contrary. There is some truth in what Dr Hunter says and important lessons for Christians activists to learn from that truth.
I agree that changing culture as such is not a mandate for Christians. That is not our mission, never has been. We are called to be faithful as God's Covenant People, living for His glory in all and what ever we do in the culture around us. We are to live according to His Law. When we do this, our lives shall be a witness to the world.
God in the person of His Son, Jesus Christ, is acting in the world. That is what He does. It is not our mandate or mission to build or advance God's work or Kingdom. He is doing that. By definition, the Kingdom is His, not ours. But when we are obedient to Him in our lives, He will use us, as His instruments or agents, to achieve His Purposes wherever we are. That will have an impact on people and institutions and in that way the culture (s) of the world around us will be changed.
That which God formed and Sin deformed, Christ will reform.