Well threads here tend to drift and it's late, so I didn't bother reading all of the replies.
But, I dated a muslim woman with "strict" muslim parents all throughout college. I know exactly what you're going through. I know all the lies she juggles with you and her family to keep up appearances that no one but her believes in. Her parents aren't retarded. If you guys start dating, they'll figure it out. So will their friends. I thought Besma and I were so smart until we were at a party (friends of the family, as always, and as usual I was either in a corner on my phone or playing with the kids because they were the only ones who wouldn't constantly leave me out of the conversation by slipping back into Arabic despite everyone being perfectly fluent in English.) So, anyway, I'm watching a few of the really young kids when one of the older ones (no older than like 12, mind you) comes up to me and goes "I know a secret about you." "What's that?" "You've got a girrrrrlfriend." "Oh yeah?" "Yeah, Besma!" I mean, come on. The twelve year old knew, and his parents weren't even really in the usual circle of people who would come to her family's parties.
And you know what? Despite everyone knowing everything, she'll never come out and say "this is Kyle. I know you're going to be angry, but he's my boyfriend." You're never going to be able to leave a message on their machine and end it with "I love you." You're never going to be able to kiss her at a party. You'll spend a lot of time alone because she can't be seen sitting next to you all night or "people will talk."
I look back at that time of my life, and despite how happy I was then, it really makes me furious now. I wasted years lying and hiding because of what she thought her parents would say. (Mind you: her parents LOVED me. I stayed at their house for a few weeks when I didn't have a place to stay, they took me to Egypt with them, and I knew all of their friends. After we broke up and she started dating other people, Besma's mother told her that no one would ever be as good as me.)
So really, please, if she doesn't have the courage to introduce you to her parents as her boyfriend, run like hell in the other direction. We've only got so much time here on Earth and it's insane to waste it on someone who doesn't think you're worth it.
Anyway, God, I've spent like half an hour on this because it keeps coming out so jumbled. (And I've had to go back a few times to erase swearwords. If I missed any, my apologies to Art's grandmother.) Just think about what I've said. And, when you decide not to listen to me, just remember later that I told you so