Monotheistic world?

I don't really like the pantheon in D&D. It's not that I find it offensive or anything, I just tend to set my campaigns in more of a grounded analog to 13th century Europe, and the pantheon kind of feels like a distraction to me. I'm going to be starting Curse of Strahd soon, and I was thinking of telling my players that if they wanted to worship a god (clerics, paladins, what have you), it would have to be Morninglord/Lathander. If they choose another deity, or play as a warlock or another class that has patron gods, I would treat those as "false gods," maybe some of them are powerful wizards who have become god-LIKE, and have some people worshipping them as a god, but wouldn't be actual gods. Maybe some of the gods are straight up demons, or fallen angels, whatever. maybe they're ghosts, liches, any number of things.

So I guess my question is, is there precedent for this? Has anyone felt similar/taken similar action in their campaigns? Is what I'm asking just totally stupid and antithetical to the entire 5e system? Let me know in the comments ;)