I think the team behind assasins creed (at least one, I havent played two) holds up a perfect example of keeping a religion significant in a story, but not beating you silly with the message. Im a christian and I actually detest christian video game makers simply because there work is bad and distasteful, in the "game" and even most of the time, in the religious aspect (I believe one game I read a brief summary of some time ago had the player as one of the original 12 disciples spreading the gospel by killing roman soldiers..... yeah......)
I think that video games are not a good ground upon which to preach to people. People have blended the christian message in other forms of media and done quite well, but Im doubtful of the video game industry.
Towards that end, I return to Assassins creed as my model for excellent use of religion in a game. If you really dont care or dont want to hear about it, then it can simply be dismissed and the game enjoyed while ignoring the undertone/theme/story whatever. And on the other side, it can help with the task of immersion and helping the player better understand the world in which his character lives.
(A fail for this, as it is in many other ways, is Dantes Inferno, Or as I call it: A massive butchering of a beloved literary classic for the sake of hooking in the spectacle fighting game crowd.)
Personally I have no problem with religious undertones and subtle messages in video games, Such as Fallout 3`s reference to Revelations 22:1, or 22:17, at the moment I cant remember which, but they both mention the river of the waters of life.