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There is little to associate the modern Republican party with, for example, Lincoln's party. Are Republicans of today going to enforce those reparations you're waiting on??? Your one-sided painting of the situation is a useless way to frame reality.
The fact that the people with the values who called themselves Democrats back then became what are Republicans today.
Stop trying to re-write history to fit a narrative, life sucks hard enough without people making stuff up to muddy the waters.
The people in the Dixiecrats are known. There are lists.
Can you name 10 that switched parties? You can't.
It is true that Civil Rights in 1964 began the switch. But it didn't really get going until Civil Rights Act (1964) really alienated Southern Democrats. Starting with Nixon's Southern First strategy, Republicans worked to appeal to them. With the rise of the religious right under Reagan there was a mass migration.
You can see https://www.history.com/news/how-the-party-of-lincoln-won-ov... to see that I'm not simply making this version of history up.
Did you have any references to it being just a "big lie"?