Because Abraham Lincoln and Andrew Johnson were Republicans.
That pretty much sums it up. The reason the Democrats lost control of the South was because President Johnson-D was able to force the Civil Rights Acts through Congress despite the efforts of Strom Thurmond and company. This is why you had Barry Goldwater (a southern state's rights candidate) in the 1964 race in the first place. The South is really more economically liberal when it comes to their political persuasions but Republicans have been able to maintain control of the South by continuing to emphasizing controversial social issues like homosexuality, evolution, stem cells, abortion, flag burning ect.