Racially I guess it depends on whether and when the 1965 immigration act happens, and how partisan support for this and future immigration laws break down.
Urban-rural and educational realignment probably still happen, as I'm guessing that social and technological progress (e.g. automation) eventually make the Northern liberal wing of the Dems the dominant wing of the party.
In general Republicans would be more in the middle of the political spectrum, while the two ends are Northern liberal Dems and Southern Dems. Abortion would still be hotly debated, but not as partisan.
This doesn't sound too different from 21st-century Dems being the party of the well-off and the poor while 21st-century R's do better with middle income voters/households.
Yet the difference would be the polarization. Had the southern religious conservative been out of the GOP, either remaining in D camp or establishing a third party, the GOP would be much more moderate, with a much stronger libertarian wing.