but the lazy narrative is that the raaaaacist south went GOP in 1964.

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

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.

Obviously LBJ was hamstrung by Vietnam, but southern conservative Democrats were so outraged by the CRA that they mostly refused to support Humphrey as his replacement. Instead, many of the formerly Solid South states voted for Wallace - an unabashed segregationist who voiced strong opposition to the CRA, and indeed the very project of racial equality. And Wallace crushed both Humphrey and Nixon in the South:

en.wikipedia.org - United States presidential election

That was the beginning of a major realignment between the parties in the region. From the Civil War through the Civil Rights Act, white Southern conservatives overwhelmingly supported Democratic candidates. Unsurprising, given the partisan alignment leading up to the Civil War. With the adoption of the Civil Rights Act in 1964, however, white Southern conservatives were outraged at the Democratic party for what they perceived as a betrayal of their preferences.

There's a lot of inertia in politics, of course - which is why this was the beginning of a realignment. Some "Dixiecrat" politicians moved to the conservative GOP almost immediately: Strom Thurmond perhaps most notably, and most explicitly, asserting in 1964 that the Democrats were no longer hospitable to people with his view. But Democrats had overwhelming majorities in most Southern states, and kept them for a while. It took several decades for that to unwind - and it wasn't really until the 1994 midterm elections that Southern conservative whites, who had long voted for Republicans in Presidential elections, really started voting for the GOP up and down the ballot.

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.