Complex sentence: After the Civil War, black Baptists were not allowed in white churches, due to segregation, and set up their own independent congregations, and developed their own state and national associations, to be free of white supervision.
Split into simpler sentences: After the Civil War, black Baptists were not allowed in white churches, due to segregation, and set up their own independent congregations. Black Baptists went on to develop their own state and national associations, to be free of white supervision.