All the Republicans I know are Federalist society/lawyer/public policy nerd types, and they are pretty open about their personal disdain for the bible belt crowd. That's the biggest tension I see. (Even the more religious ones tend to be "high church" types---the Catholic church is becoming hegemonically dominant among some intellectual conservatives---but I'm not totally convinced that they sincerely believe in the Deep Magic rather than trying to anchor themselves in the West.)
I sense some unease between more internationally oriented, and more "America first" oriented Democrats. However, overall it seems they've been better able to reconcile the different interest groups that make up their base.