A few scriptures to refute this idea of making the church more "relevant" to reach the culture. Plus, the church is not going to be relevant to a culture who does not seek after God nor loves Him. The church body goes out into the culture and shares the message of the Gospel so that they can be converted and join the body of Christ.
"Adulterers and adulteresses! Do you not know that friendship with the world is enmity with God? Whoever therefore wants to be a friend of the world makes himself an enemy of God." (James 4:4)
"Preach the word! Be ready in season and out of season. Convince, rebuke, exhort, with all longsuffering and teaching. 3 For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; 4 and they will turn their ears away from the truth, and be turned aside to fables. 5 But you be watchful in all things, endure afflictions, do the work of an evangelist, fulfill your ministry." (2 Timothy 4:2-5)