There were a few Republicans in the South and they did not support civil rights.
I grew up in the segregated South, and a couple of parents in our elementary school were pointed out because they VOTED Republican. Straight ticket.
I cannot remember a single Republican congressman in the Deep South from the late 1950s through the Civil Rights Act. Admittedly I don't know every politician in the South, but I'm pretty sure there were none in Georgia or Alabama. About the only thing I can think of is maybe a lone Pubbie in Atlanta or Charleston . . . maybe . . . but I doubt it and I'm sure I would have heard about it, because my parents marched at Selma.