What made Mississippi and South Carolina vote more Democratic then the Other Solid South states during this time period?
More vote suppression.
Also the demographics of both states. There were no Appalachian areas that provided a GOP bastion or even a slightly more Republican enclave like VA, TN, NC, AL and GA. TX had Germans, some of who voted Republican, LA has pro-union enclaves and cajuns and AR had the Ozarks. South FL had a property boom in the early 20th century driven by out of state rich people, some of who would be Republicans from NY or ILL.