While the south was under an apartheid regime many Republicans ("Rockefeller Republicans") were to the left of Democrats ("Dixiecrats.") This is no longer the case; every Democratic senator is to the left of every Republican senator

Desegregation isn't irrelevant to what has happened to American politics- but this doesn't have anything to do with where senators are on an arbitrary political spectrum. The particular manifestation of the left-right political spectrum you have in mind here is the invention of the post-segregation political climate. Pre-desegregation issues didn't break down into positions corresponding to our current political spectrum.