how did church and the naacp help end segregation in america?

Answer 1

I would like to think that J.F. Kennedy as then president, signing the bill outlawing segregation and his brother then Bobby Kennedy the Federal Prosecutor following through and starting to charge violations against segregation was very prominent in the ending of segregation. The Church of course had it's followers and NAACP.

Kennedy started sending troops in segregated states and ending this behavior. It was even theorized that this was one reason they were both assassinated.
By the KKK but, was never proved.

Answer 2

I can only honestly answer the church part of your question. The church used values that were common to both sides of the conflict to make the oppressor side feel ashamed. The folks who wanted segregation could not escape condemnation from the scriptures they cherished, once the sin was pointed out to them. Also under M.L. King's leadership the Civil Rights Movement never voiced any hatred for the oppressors. He knew that projecting love toward them would punctuate their sin.