This entire thread is discussing an alternative given that region lords can't build temples to other religions.
Yes, this entire thread is about making something possible that the game does not allow. Please do as I asked in my first reply and stop thinking about the "how" and think about the "why" for a moment. Why does the game not allow you to build any temples of any religion? That restriction is there for a reason, you know?
Once you accept the premise, you'll understand that both rotating lords and rotating religions is a clear and obvious abuse of the game mechanics to circumvent restrictions of the game mechanics.
If you insist that there should be a way for having multiple temples of multiple religions in the same regions, then having them built by priests instead of lords would be the proper solution. That's a solution that makes sense and can be discussed, but it does have consequences that you should think about as well.
