Mark Driscoll, in summary, gave three helpful applications for the gospel and culture.
1) Some things we must reject outright from culture. These are things that are completely incompatible with God and the Bible. There can be no compromise on these things. Examples may include homosexuality, abortion, porn... these are moral sins that are found in the commands of Scripture.
2) Some things we can receive from culture. These are things that God has given humanity the intelligence and innovation to create and bring about for the common good. God sends rain on the just and unjust (Matthew 5:45). An example is the use of medicine, doctors, etc.
3) Some things we must redeem from culture. There are some things that were morally good or neutral but culture has corrupted. They must be reclaimed for God's purposes. Examples may include certain technology or inventions, sex, gender and relationship views and others.
These 3 categories are helpful in trying to discern how a Christian is to relate to culture without watering down or abandoning the heart of the gospel.