How did the different religious institutions in the USA address racial segregation/equality? Especially with regards to the Catholic Churches' stance

by Aeschylus-
Aeschylus-

I'm watching the film Doubt (2008) and in the film a black child is attending a Catholic School during the early days of the LBJ presidency, in the film they're discussing a school dance and I was wondering how the potential interracial courtship would have been dealt with strictly from a religious perspective.