The South voted for non-major party candidates on multiple occasions between 1948 and 1968. Rather than realignment towards either Republicans or Democrats, there's every chance you instead get a distinctive Southern party, especially if it could absorb upscale Republican voters in those states in the same way as the Republicans absorbed reactionary Democrats in our timeline.
The trouble with this is that upscale Republican voters in Southern states weren't ideal fits for a right wing Southern southern party, especially in places which were more economically prosperous and had transplants. Nixon won places like DeKalb, Cobb, Lexington, Fort Bend, Mecklenburg, etc. over Wallace. NASA engineers and bankers in the South were pretty racist but the more overt populist stuff had a weaker appeal there, in much the same way that the descendants of these people only abandoned the GOP when someone like Trump came to the fore.
As an aside, does anyone know why Davidson County TN voted for Wallace? Obviously a narrow thing and the result of a three-way split, but it's basically the only fast-growing sunbelt urban county in the South to vote for him (barring Duval, which makes more sense).
