"Social correctness" is not compatible with biblical Christianity. True Christians are guided by absolute moral principles espoused by Jesus Christ. The truth doesn't change- social norms do.
You have it backwards - it is society (sick culture) that is driving uncommitted Christians into buying its poison.
There is nothing that could happen in the Churches that isn't internal. Ministers, in many cases, preach a social gospel. They do not discipline Church members. Ministers themselves act like unsaved people. What is happening in the Churches is a lack of leadership to guide the Christians who need someone to guide them. That is the job of pastors.