Not sure I've ever heard a conservative give a decent response to the simple "so why did Strom and other dixiecrats leave the democrat party and join the republican party after the CRA passed?" question. And why did the south go from a democrat stronghold to a republican stronghold? And what was Nixon's "law and order" all about?
Thing is Strom Thurmond was the only one who did change parties. Most of the swaps like Phil Gramm, Richard Shelby, etc. all were elected in the late 1970s/early 1980s.
And the South's status as a GOP stronghold has been oversold by focus on the Presidency and may be running out of steam. The GOP wasn't even a viable party in the South until the 1980's, and didn't start controlling state houses until the 2000s.
I think general Social Conservatism/Religious Right Rise/etc. explains as much, if not more than trickle-down racism. The northern Reagan Democrats abandoned at about the same time because of the McGovern-Mondale-Jackson "hard-left" swing of the Democrats outside of History's Greatest Monster.
"Law and order" was definitely a coded statement about the race riots, that's the entire reason Agnew got on the ticket despite being a Rockefeller Republican, he stood up against the black establishment in Maryland so he became acceptable in the South even though he was easily less conservative than Nixon.