"Follow the money."
Of course the Democratic Party's Southern sect was violently anti-black. This does account for alot of the Party's lock on the South through the 20th Century.
But so far FDR has only been lightly aluded to...and he's the biggest impetus behind the Democrats' staying power in the South: The New Deal's agricultural policies are still as much sacred cows to the rural South as is Social Security. These are folks who didn't like the liberalization of the Party. They didn't like its Dovish turn. They sure didn't like its adoption of Civil Rights.
But they're still taking the subsidy checks...and still voting for them--trying to keep their way of life from drying up. Republicans haven't endeared themselves in being pro-free trade, either. It's only in the white urban and suburban centers of the South that the Republican transformation really has strong roots.
It was with FDR that the Democrats began winning the black vote.