Like I'm certain some others have already said, it really depends on the persons involved and their level of faith. I know people in stable relationships who are of different religions, and they've been together a while. I know someone who's strongly Christian and is with someone who isn't religious at all, and they just take it in stride and are fair to the other's beliefs.
Though, I also have a close friend who's family is so religious, that she ended a 6 year relationship just because her boyfriend wasn't religious and that was straining on her faith, and her family's faith. They wanted her to be with someone who was supportive, and would go to church gatherings with them. She was depressed for a while that they split, but she claimed it just couldn't work long term.
From my personal standpoint, my ex was raised Catholic, and had a lot of Catholic guilt going on and there were multiple times when I thought his family was insane for pushing such things on him. Didn't care for how religious they were, and some of their views. So IMO, it can be difficult, but if neither side is too extreme, I also believe it can work.