I have a friend who is Muslim and she did not always wear her hijab, but then I didn't notice when she wore it versus when she didn't.
She was one of the most open-minded people I've ever met, and we actually bonded and became friends over someone else's misconception about what my religious beliefs are. She was actually the person in the room who got what I was saying because she didn't have the religious stuff the other people had in their heads that kept them from hearing what I was really saying.
She had no real knowledge of Christianity and I had no real knowledge of Islam, so we were both delightfully free to ask questions of each other without feeling that the other person was proselytizing or preaching.
Although I don't know what the Quran says about it, my friend was a lesbian and she considered herself married (marriage not being legal between same-sex couples is why I'm stating it this way) to a Buddhist. She had some horrific experiences when her family discovered that she was a lesbian.
She told me that her experiences with being persecuted by her family because of her sexuality strengthened her connection to her religion, rather than causing her to discard it or become bitter because of her treatment.
I suppose that like all other religions, you have people who go through the motions because that was how they were taught at home to behave, you have some who are "posers" for whatever personal reason (job security, desire to fit in with those around them), and on up in terms of intensity of belief until you reach full-blown zealot.
Zealots, statistically speaking, are found in every religion. (Yeah, I know I'm running a real chance of being told how wrong I am, and go ahead.)
I don't think that Carterpot's statement was racist, but perhaps it could have been stated a bit more clearly. Hijabs hide only the hair--but I've heard of many Muslim women who wear the full veils that have very elaborate makeup on underneath. And that they love wearing the very frilly and lacy undergarments. I suppose if I were limited by what I could wear on the outside, my own tendency would be to dress rather punk underneath. Matter of fact, I'd feel more free to wear what I'd want to under those robes since it would be a secret to everyone I'm meeting!
You have real potential for an interesting, dynamic character. Good luck fleshing her out!