Well, there were notable concentrations of racially moderate whites in New Orleans and Atlanta, even back then. I believe that fairly significant black voting continued in Atlanta during that time as well. That could be enough to explain Louisiana and Georgia being over 10%.
Overall, this is ambiguous because some of the Republican candidates during that time were decidedly populist-Progressive and others were decidedly conservative. Alabama in 1920 is particularly interesting because Harding was known as one of the most racially open presidents during that time period. There must have been a strong anti-Progressive faction in Alabama then.
Also, AL and MS seem to often be lumped together, but it appears that Alabama was much more Republican relatively, especially in 1900-1928. MS and SC seem to be inconceivably monolithic.