My personal guess is the switch occurred during the New Deal when the elected portion of the fracturing Democratic party embraced the power of Washington over the states.
Republicans were in favor of Civil Rights leglislation in the 60's though.....although a strong war declaring President seems consistent with their views since the 80's.
HELP! Point me to some reading please.
It was FDR who earned the Black vote in large numbers. The New Deal was indeed part of that, also improving the lives of Blacks. Also, Warm Springs connected FDR to Rural Blacks. It was a turning point, for Dem's relationships with Black Americans, who feared Southern Dems of the day, many of whom were racists and supporters of the KKK.
In fact, former KKK-friendly (maybe) Truman had Black Leaders worried. So Truman met with them, and despite his own racist tendencies, was true to his name, and lived up to his promises to them, carrying on the FDR tradition.
Additionally, albeit not immediately an issue in the minds of Blacks, the last true Lincoln Republican was Teddy Roosevelt. And indeed, the Republican Party of today, perhaps because of gains among white bigots when LBJ signed the Civil Rights bill, have made the white male voter a core constituency, and frequently use the keywords that appeal to white bigots ... as well as oppose minority rights issues reflexively.
Dems lost the South, for generations, due to the Civil Rights bill
Reps lost the future make up of America, maybe also for generations, by making racism a core aspect of the "Republican" brand.