The D’s who voted against the civil rights act were the Southern racists. They were soon without a party. Many became R’s like Strom Thurmond. Along these lines, the parties realigned over time after 64, with the R’s becoming the party of the white south and the D’s, the party of the minority. The first shot over the bow on that was Goldwater’s stance on the civil right act, reversing R policy, and lo and behold, guess what, he won some southern states that hadn’t voted R since reconstruction. The process continued under Nixon and came to full fruition under Reagan, who carried the south over a D southerner. Reagan was not himself a racist at all, yet the Lee Atwaters of the world knew where their bread was buttered and his campaign also addressed white grievance ergo welfare queens. Clinton did try to triangulate to the right during his tenure, but nowhere to the extent of the R’s.
P.S. Almost all of the R’s who voted for the CRA were northern moderates who have been driven almost to extinction in the party.