There are a lot of stubborn people in the world, so were there significant numbers of people that said ‘I’ve always voted this way so I’m going to keep doing it’ despite parties not being representative of them any more?
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African-Americans didn't suddenly switch to becoming Democrats in the 1960s. It began in the 1930s under FDR, who came up with the idea of winning over voters of a certain ethnicity rather than a region. He made some progress on civil rights, but hesitated to do more, not wanting to alienate the Dixiecrats.
What solidified African-Americans as a Democratic voting block was Barry Goldwater, one of the few individuals who voted against the Civil Rights Act of either party. In 1964, he lost by perhaps the greatest landslide in electoral history, winning only the Deep South and his home state of Arizona. He argued it wasn't the Federal Government's business to say what a state could and could not do.
When it comes to the Civil Rights Act, almost everyone outside the South voted for it, Democrat and Republican. Southern Democrats were the ones who did everything in their power to stop it, save for a handful.
Nor did the South become a Republican block after this. In 1968, those who wanted to keep segregation voted for George Wallace, not Nixon. In 1976, Carter swept the southern states, save for Virginia. Reagan's closest victories in 1980 were Massachusetts, Tennessee, Arkansas, Alabama, Mississippi, Kentucky, and South Carolina.
They didn't start becoming a Republican block until 1984 and beyond. Even then, Bill Clinton won Arkansas, Louisiana, Georgia, Tennessee, Kentucky, and Missouri in 1992. In 1996, he added Florida to that list.
A few Dixiecrats became Republican but most stayed Democrat until they either retired, died, or were voted out of office. Biden caught a bit of heat for this in the primaries, but he's been in politics over half a century. In the early part of his Senate career, there were still segregationists in office.
If anything, it wasn't until the 21st century that the southern states became reliable Republican voters. Except for Virginia, that is, which has become a Democratic stronghold.
Neither the Republicans or Democrats are running on a segregationist policy today. We still possess many racial issues, but the debate's turned into "How do we fix this?" not "Keep these people in their place!" We've come a long way since the days of Jim Crow.