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Main article: The Southern Strategy

Historically, the Republicans had freed the slaves, driven civil rights (1866, 1875, 1957).
JFK wanted to rehabilitate the Democrats and his own image (Hitler or Communist sympathizer). So he copied the civil rights acts of 1875 and 1957, and he pushed The Civil Rights act of 1963.
That was blocked by his own party until he took a bullet. And then it took the greater support among Republicans than Democras to get it passed. Johnson only supported it in order to, “have those niggers voting Democratic for 200 years.”

The Repubicans created the "Southern Strategy" to appeal to the broad groups alienated by Johnson's radicalism, identity politics, central authority and tax and spend New Deal. (Carpet bagging northerners and big government was still unpopular in the South).
Racist were a small percentage of the electorate, even in the South. And they would never be attracted to the Republicans with their richer history of defending civil rights.
The Democrat Party had no defense, so they turned to Saul Alinsky and Joseph Goebbles "big lie", and used the Frankfurt Schools Critical Race Theory: if you can't divide by class, try race instead. So they called the Republicans "racists", and rebranded the Republican's Southern Strategy as, "a strategy to appeal to racists". Which makes no sense to anyone but miseducated or ignorant leftists.

Lifelong racists weren't going to switch parties with such stalwarts in the DNC as George Wallace, Joe Biden and Jimmy Carter, and the rich history of the Democrats and the KKK. Especially over a law, that couldn't get passed without the Republicans higher support.
Which is why Democrats won the South in 1968, 1976, 1988, 1992, and 1996. (Nixon landslided in 1972, and Reagan did in 1980 and 1984 -- so they carried everything).
It wasn't until the year 2000 (32 years after "The Southern Strategy"), that Republicans started really carrying the South regularly.