I don't think anyone is arguing that the parties completely switched, but both parties used to be much more ideologically diverse and have both liberal and conservative factions. There was a robust liberal wing of the GOP that was primarily based in the Northeast, along with a large contingent of conservative Democrats mostly from the South.
Now, most Northeastern liberals are Democrats and most Southern conservatives are Republicans.
A Conservative Republican Senator voted against the 1964 Civil Rights act. And no, he was not Barry Goldwater.
It was a guy named Norris Cotton; who otherwise voted for the 1965 voting rights act.
He voted to end cloture though. There were other Republicans not from the South who voted in favor of the filibuster, which was really the more important vote.
The 6 Republicans were: Wallace F. Bennett (Utah), Barry Goldwater (Ariz.), Edwin L. Mechem (N.M.), Milward L. Simpson (Wyo.), John G. Tower (Texas) and Milton R. Young (N.D.). The following Democrats joined 18 from the deep South in voting against ending the debate: Alan Bible (Nev.), Robert C.Byrd (W.Va.), Albert Gore (Tenn.), Herbert S. Walters (Tenn.) and Carl Hayden (Ariz.), dean of the Senate, who had never voted for cloture
https://library.cqpress.com/cqalmanac/document.php?id=cqal64-1304621