That would indeed be a lazy narrative....which is why no one actually argues that.

Other than the people who insist that everyone in the south votes GOP Because Raaacism, you mean.

The actual, nuanced argument is that the passage of the Civil Rights Act in 1964 created a schism in the Democratic party, between liberals that supported the CRA and (mostly) southern conservatives who opposed it. That didn't seriously affect the 1964 elections, which was dominated by the death of Kennedy and the very specific issues raised by Goldwater's candidacy. But it had profound effects in the 1968 elections.

That's not what was argued. The argument was the racist southern voters all shifted to the GOP in 1964 and stayed there. As you point out, it's far more nuanced than that, and when one looks at, you know, actual voting patterns we see that the south wasn't solidly Republican until more than 3 decades after the CRA passed.

No lefty ever squares the circle with the fact that Eisenhower was the first President to push for broader reform and the CRA passed with more Republicans than democrats, but as I said, it's a lazy trope that's meant to be an argumentative woobie.

Ultimately, though, the demographic of the American electorate that was most resistant to the passage of the Civil Rights Act were white Southern conservatives. That demographic was an integral part of the pre-1964 Democratic party; it is now the core of the modern Republican party.

And here's where the trope comes back in: is today's voter the same as a pro-segregationist from 1959? The answer is 'no', and it's again a very lazy thing to assume that people don't change culturally over time.