Culture is "the sum total of ways of living built up by a group of human beings," Random House Dictionary. For this answer, culture means the behaviors that society considers acceptable. These standards of behavior are also called norms of behavior.
James 4:4: "… know ye not that the friendship of the world (culture) is enmity with God (Gospel)? Whosoever, therefore, will be a friend of the world is the enemy of God." This shows that there is a difference between the standards and practices of the world and God's righteous standards. Although there are some standards of behavior that both culture and gospel uphold, such as murder being a hateful crime, there are many ways in which culture and Gospel are not in harmony.
There are inevitable conflicts between culture and the Gospel. God's standards do not change. James 1:17 says, "Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom is no variableness, neither shadow of turning." On the other hand, cultural norms established by men are relative and may change. Therefore, the Gospel and culture may clash as to what is acceptable.
The Bible has many examples of those who kept a righteous standard while living in an evil culture. Noah worshipped, trusted, and obeyed God by building the ark. Those in that culture laughed and scoffed at him. While in captivity, Daniel refused to partake of the Babylonian food, which was a part of the culture.
Jesus gave us encouragement to continue our struggle against a culture that encourages us to lower our standards or to follow the crowd. By remembering the Lord's Prayer which says "Abandon us not in temptation", we can be strengthened in our struggle to obey God. Jesus prayed directly for his followers in John 17:15-16, "I pray not that thou should take them (his followers) out of the world, but that thou should keep them from the evil. They are not of the world, even as I am not of the world." Jesus prayed for his followers to be protected by God as they struggle against world (culture). He gave his followers hope when he said, "In the world ye shall have tribulation: but be of good cheer; I have overcome the world," John 16:33. What courage these words give the followers of Jesus! We too can overcome the world.​