Following the Civil War it was Republicans who repeatedly pushed legislation through Congress that improved the legal, civil and cultural status of former slaves, and it was the Democratic Party that fiercely opposed these measures. And not just Southern Democrats for most of this period but most Democrats from the North to the South. As the left took over the Democratic Party during the 1960's and 70's the fundamental character of the party changed to one that was openly hostile to all the things Southerners held dear. Not just a position on race, but on religion, culture, tradition, and economics.
Dixiecrat's became Republicans not because Republicans adopted segregation -- there wasn't a single instance of Republicans putting any of that in their party agenda. They became Republicans because the Democrats were repelling them in so many other ways culturally. Democrats famously had become the party of "acid, amnesty, and abortion", issues that were repellent to Southerners outside of any consideration of segregation. In fact, the Republicans offered the Dixiecrat's very little, but what they did offer -- a respect for most of their cultural and spiritual values -- was enough. Republicans were surely the lesser of the two evils at the time for Southerners.
The fact of the matter is that Dixiecrat's were forced to give up segregation as an issue. Wallace's failure to get more than 9% of the vote, with which Nixon became President anyway, demonstrated how moribund that issue was.
As Jonah Goldberg writes:
The bigotry aimed at the South never ceases to amaze me. Indeed, it is astounding to me how the left tells us we need to understand the nuance of, say, the Jihadi mind in all of its shades of gray, but when it comes to the voting habits of law-abiding white North Carolinians all you need to know is that if a white hand pulls a lever for a Republican politician, that hand must be attached to a racist, and that racism guided the hand to vote for a Republican. The South is a complicated place. Racism was certainly its central shortcoming, but it was hardly its only feature. That so many people can only see the racism, even as its half-life accelerates, says more about their myopia than it does about the region it casts its gaze on.