"The big break didn’t come until President Johnson, another Southern Democrat, signed the Civil Rights Act in 1964 and the Voting Rights Act in 1965.
The change wasn’t total or immediate. During the late 1960s and early ‘70s, white Southerners were still transitioning away from the Democratic party (newly enfranchised black Southerners voted and continue to vote Democratic). And even as Republican Richard Nixon employed a “Southern strategy” that appealed to the racism of Southern white voters, former Alabama Governor George Wallace (who’d wanted “segregation now, segregation tomorrow, and segregation forever”) ran as a Democrat in the 1972 presidential primaries."
So whenever someone mentions the Democrats creating the Ku Klux Klan, and Martin Luther King was a Republican, feel free to read this (real) bit of history.