This ignores the realignment of the parties in the 1940s. See the formation of the States' Rights Democratic Party (Dixiecrats). https://en.wikipedia.org/wiki/Dixiecrat
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"?