Viking Conquest has Pagan and Catholic religions. I know it plays a part in how certain people like you, including villages, towns etc.
If you follow the Old Gods for instance; you can sacrifice an animal before battle to gain morale, or lose it if the sacrifice shows a bad omen.
You can erect Pagan shrines in villages (that's all I've encountered in my short time) to sway the population to the religion. This can cause riots if it's opposed too heavily. The more a village believes the same as you, the more likely you'll be able to recruit men to your army.
Anyway, that's a tiny experience I've had with religion in that game.

King arthur the role-playing wargame? OK, it is mostly a Total War clone, but it takes the "role-playing" part of the title seriously with quests, detailed knights, weddings, chose-your-own-adventure with multiple endings, magic items, plotlines...

The religions are more "fantasized christianity and old faith" than the real deal, but they have a major part in the game, and pagan-christian gauge is (along with rightful / tyranical) one of the major axix of the alignment system. It unlocks new buildings, new spells, new troops, tell you who will go to war with you, how you will deal with the faeries, which knights will be loyal to your king.

Many of the decisions you take during the game (like promising a druid his faith will be protected in your land in exchange for his help, or sacking an abbey) will have a direct impact on gameplay. Cool game if you like a mix of tactical battles and RPGs.
Some bugs, though.

Hmm, that's actually kinda cool.