You have two distinct problems, but they boil down to the same thing: it is commendable to stay true to your nature, but the same applies to other people. Attraction between a homossexual and a heterossexual always ends in disaster. We even have a name for people for which it can work: bissexuals. The same applies for (a)sexuality.
So if the girl really is het, I'm not optimistic about your prospects. But on the other end what do you know? Perhaps she is not het, or has bissexual tendencies, so you might as well try your luck. As long as you are aware of your low odds, it does not hurt to try. As for the assexuality issue, you'll deal with it when it becomes a problem.
For me, the best attitude for you would be to do what many homossexuals do: meet like-minded people via internet, or at lesbian friendly bars/associations/etc. This is exactly what people who want to meet people from the same religion do, there's no reason you could also not do it. In this way, you beat the fact that you are a minority. As for the assexual aspect, same thing: meet assexuals over the internet or IRL. There's plenty of ressources available, check this http://www.asexuality.org/en/