One of the worst things that Game of Thrones has enabled (involuntarily) in a particular kind of almost exclusively male nerd is a permission structure for going UMM WELL ACTUALLY at "unrealistic" depictions of medieval life (which aren't even unrealistic, you're just an undereducated twat)
IDK, I'd say the massive central role of Christianity and its relationship with politics and legitimization of authority is extremely important in the IRL middle ages and if your RPG setting doesn't have a good parallel to that, might as well go nuts with whatever else.
The only RPG I've ever seen that depicts the middle ages historically accurately is Ars Magicka and that's because depicting the middle ages in a way only people with university degrees would appreciate was kinda the whole point.
Also haha jokey sidenote: I have always associated the Middle Ages less firmly with Christianity than other people tend to because I grew up in Europe's Last Pagan Country (tm)