They don't need to be that though. Honestly for all of 5e's flaws, I think one thing it does far better is that there is a clear distinction between Clerics and Paladins. Clerics get their power from religion, Paladins get their power from swearing an oath. Religion doesn't need to be a part of it at all.

Like, if you told me there was a class called "champion" in Pathfinder and I knew nothing else about that class, I would assume it's the champion of a cause, not of a religion.