The 1968 Presidential election saw the Democrats lose the south to an Independent run. 1972 was a landslide for Nixon due to the blow back on Democrats from the Vietnam war. The 1976 Election saw the South right back to voting Democrat again.
Twelve years after the CSA was passed and the Democrats still won all but a handful of Southern voting districts...
...and the Republicans won a landslide in 1972 because of Nixon's promise to end the Vietnam war.
The narrative that racist Democrats fled to the Republican party in the face of righteous Democrat civil warriors is a fairy tale that Democrats tell themselves to rationalize why they lost a decades long grip on government to the Republicans.