First of all, I agree with the one-itis comment, you definitley have one-itis. The big tip off to that is your "I know there is other girls, but this one is different/special" remark.
That aside, religion is something very odd to mess with. If a girl is very religious or her family is very religious, you will never be fully accepted. EVER. Even if you "talk things over" and somehow talk yourself into a relationship with this girl and get her family to not hate you, they still will never like you and things will never be as good as if they were if you were their religion.
If religion is important to you or her in a future context and in a practicing the religion way, and you are of different faiths, it will cause more problems than its worth. Its almost as taboo at that point as interracial dating is (to people who are racist or sense a very strong connection to their race) in the sense that whatever arguments or fights you will have down the road will eventually boil down to this topic or area and its a topic that will never resolve itself.
And that's the key, see a topic like having political disagreements or movie taste preferences that are different, are topics that can resolve themselves. You eventually can come around to her side or her to yours, or you can find a negotiating position in the middle. There is no negotiation with religious beliefs because by definition they are solid and immobile. Therefore, no matter the argument or discussion, you will never find a compromise and there will always be tension.
Now that you know this, if you still want to pursue a chick who has a different faith and its important to her and her family, and they disapprove of your faith and don't want her to date outside of it, you are opening yourself for a big can of worms.
And don't even try that "maybe we can just kiss without being a relationship" or the "I don't even want to bed her, just do other stuff" fallacy crap. We all know that those are gateway things to other things. First of all you have oneitis so you're obviously like in love with this girl, so you are denying your true intentions if you say you'd be happy with just being friends with benefits with her.
And if you were happy with a FWB arrangement, you'd be lying to all of us if you said you didn't wanna have sex with her -- and why wouldn't you, especially if you are FWB since thats what the benefits part of the arrangement is, the sexual stuff.
So basically, don't try to trick yourself that you'd be happy "if you could just kiss her" or whatever, because you won't be. You think that now, but once you reach that milestone and the novelty of kissing her has worn off you WILL want more. Same with FWB. Once you start getting intimatley involved, you're going to want the relationship (especially since you are so into the girl) and you WILL get attached to her.
So to recap:
1. You have oneitis
2. Religious differences are trouble
3. You won't be happy if you don't get what you want, so go get what you TRULEY want and not what you think will "hold you over" for now because if you do that you will eventually want more, and if you know more is not possible, then its not worth to begin with.
guarenteed!!!