The first thing that springs to mind is the problem of breaking suspension of disbelief.
Personally, I'd find it harder to get into a game if I had to run by a Church of Scotland Minister on my way to pick up some gear, but not everyone is going to share that view. The second thing that springs to mind is a bit more obvious. The reason in-game religions appear to be fuzzy and ill-defined is that it's a lot harder to take offence at a religion dreamt up by a few games designers, than it is with an actual religion which may or may not have a an antagonistic history with your own beliefs.
While I do think there's a place for more religion and faith in MMOs, I'm pretty sure that bringing real-world religion into them is a big mistake. How many religions should you bring in? Where do you draw the line and strike a balance between a healthy amount of choices for your players and avoiding accusations of excluding one or more religions?
I remember reading somewhere a quote by Anne McCaffrey, who explained to a fan who maintained the culture on Pern could never have survived without religion, that it was her world, therefore if she decided there was no religion, then there wasn't any. In short; keeping religion out of the equation keeps things simple. By sketching in the general details of a religion in an MMO, developers can avoid accusations of discrimination. Although World of Warcraft has Priests, Bishops and Cathedrals, the Church of the Holy Light has enough of the specifics left blank that there's no way you could accuse it of being a front for Roman Catholicism, for example.
I'd like to see more games making use of religion and faith as hooks to draw players further into their games. We wouldn't need much – give us the basics of a few well-thought out religions and faiths in-game, but make them an important part of the game and our imagination can do the rest. I'm not a particularly religious person in real-life, but I am the kind of gamer who hungers for more story. I'd love to see more of anything that could give my MMO more substance.
While I do think that there's a place for religion and faith to be incorporated more into MMOs, sadly I don't think that adding real-world religion is a good idea. We have a hard enough time with the usual varieties of idiots polluting our games just now. If we were to add real-world religions to the mix, we'd only be giving them something else to hate on, besides race, sex and sexual orientation.
Besides not being very religious, I'm also not very optimistic about human nature, and until more people start to 'play nice' in MMOs, real-world religions would be a big mistake.