Hmm. I don't see that I'm getting my point completely across.
I think I need to offer an example, and so I will have to mention a game after all.
Take Warhammer Fantasy Role-Play (specifically talking about the rpg now, not the minis game. And even more specifically, I'm talking about the original 1st edition).
At first blush, you might think the Old World is much like the standard D&D worlds as regards religion, the gods, and magic. You have priests. They get spells. The gods have portfolios, interests, enemies. And so on.
Yet, everything is different.
The gods never run around in the game world, stealing your daughters, bedding your wife, and turning your sons into monsters. For starters. So you can never say for sure the gods exist. That is a deliberate design choice made by the authors, who understood how this actually helps you portray a religious character. Because with uncertainty you can have actual faith.
But there's more. How about the spells the clerics and priests cast, you might wonder? Well, here's the clincher - the game presents a possibly conspiracy theory claiming that all magic actually is chaos energy. That is, the black stuff, the corrupting influence, the daemonic energies.
This is what I'm talking about. You have a group of game designers that realize the naive D&D approach will not and can not lead to believable belief. And so they offer an out.
Not to shaft religious-minded players. To enable them.
(It doesn't matter whether this theory is actually true or not. The important thing is that despite having gods like Odin (Ulric), Poseidon or Neptune (Manann), Hades (Morr), and Athena (Verena), you can still have people doubting the existence of the gods, and even the existence of goodness itself.
Which is precisely what you need for the reverse - religiously devout characters.
Here we have a game that intelligently realizes that there must be uncertainty for faith to exist. I'm not saying you should play WFRP. That's just my example here and now - there are plenty other games that share that crucial insight in what you need to portray religion in a believable way.