1950s-60s Southern Democrats were not monolithically hardline segregationists, especially outside of "Deep South" AL/MS
And it is towards the end of the 1960s and into the early 1970s that you begin to get into the "New South Democrats" like Jimmy Carter, Terry Sanford etc and these people depended on strong black support combined with a "strong enough chunk of white votes" to win elections.
I recently watched some 1986 election night coverage and one of the Senators (some guy named Joe Biden) that they interviewed talked about how "there is a new ball game in the South" and that they didn't need to nominate a conservative to win the region but needed a moderate from the region who could combine a coalition of blacks and whites to win the region, and that this was essential to winning back the White House.
The thing is you don't just turn on a dime and have these people manifest out of thing air. Instead, they came from the populist/progressive wing of the party that had long existed in the region and had previously accepted Jim Crow as the reality (in some cases going into the race to the bottom like George Wallace did and even more so Theodore Bilbo), but in some cases they went the other way and this was one such example since Ralph supported Civil Rights aggressively and TX had a tradition of being not quite as excessive with the repression.
