First: the timing of the transition. Let’s take Alabama. In 1960, it voted for JFK, who was perceived as weak on civil liberties. Then in 1964, it went Goldwater because LBJ didn’t appear on the ballot. In 1968, it voted for Wallace, who was not a Republican, he was a New Deal Democrat. In 1972, it voted for Nixon. But Nixon won almost every state, including New York. In 1976, Carter blew out Ford in Alabama, winning by 13 points, compared to his 2.5 point margin in New York. That shows the Southern Democratic contingent was alive and well as of 1976. It voted for Reagan in 1980, but by one point, compared to Reagan’s 9 point margin in the rest of the country. Carter ran more closely with Reagan in Alabama than he did in New York.
The question is: if the 1964 Civil Rights Act caused a mass exodus from Democrats to Republicans, why was a Democrat outperforming in Alabama compared to New York even by 1980? Democratic support for the Civil Rights Acts May have broken the “solid south” but that doesn’t mean those people became Republicans—who also supported civil rights. Other things needed to happen.
What those things were: they’re related but not the same as “civil rights.” “Civil rights” isn’t a single policy, but a range of policies with different ideological implications. Republicans strongly opposed de jure discrimination, and supported civil rights laws that eliminated such discrimination. But by the 1970s, the fight had moved to different issues: forced bussing, affirmative action, etc. And the race riots of the 1960s, and skyrocketing crime in cities, made “law and order” hot-button issues. Nixon and Reagan capitalized on southern views on those policies.
Saying that Nixon’s “southern strategy” was rooted in opposition to “civil rights” is a very Democratic way to look at the issue. Nixon helped champion the 1957 Civil Rights Act through Congress. He never backtracked on that. What he did was promise disaffected southern Democrats that he would not use the force of government to integrate private society, and would maintain law and order. (So did Carter, by the way.) It’s maybe fair to say it was an appeal to southern racism, but it was not ideologically inconsistent with his support for the civil rights act, and ideologically consistent with conservatism in general. (I happen to agree that you need affirmative action to erase previous discrimination. But I think it’s not intellectually honest to pretend that opposing affirmative measures to equalize society is on a continuum with opposing measures to eliminate de jure discrimination. They’re categorically different things.)
Apart from that, some reasons were in fact unrelated. Starting in the 1970s, the southern economies moved from agricultural to commercial. Southern states realized they could outbid northern states for business though low taxes and low regulation. Southern cities like Atlanta and Charlotte boomed during this period. That dissipated the New Deal sentiments that had previously tied the south to Democrats.
If you asked me what caused the modern Republican “solid south,” I would not say “the civil rights acts.” I think that an unwarranted attempt to tar modern conservatism in with segregationism, which is especially galling because New Deal liberals were in an alliance with segregationists at that time. I would say the proximate cause is the culture wars of the 1980s and 1990s, and the economic development of the south as being reliant on low taxes and regulation as a way to outcompete the north.