Yeah, I dont see how his faith impacts his ability to do an autopsy on a dead guy, gay or not. Unless, of course, there is some hidden Mormon prohibition about touching dead gay dudes that we all dont know about....
Well, if it's hidden, it's hidden to us as well.
(I also don't see how any religion can be classified as more "far-fetched" than others. Once you are willing to accept the concept of a divine being of any sort, the rest is just details, and I don't see how something holy happening in Missouri is any weirder than something holy happening in Jerusalem. But that's just me apparently . . . )