They basically switched places with Dixiecrats.
That's right--almost all Dixiecrats either retired or went to the GOP, and almost all Rockefeller Republicans either retired or went to the Democrats. This, in turn, made American politics much more polarized.
Indeed. I would place the factions as such:
Rockefeller Republicans: left
Democrats: center-left
Republicans: center-right
Dixiecrats: right
So essentially, the parties became united on ideological grounds, rather than cultural, religious, ethnic, and income backgrounds.