People will spout all kinds of nonsense on here but I am going to give you the facts as someone who grew up in a heavily brown area in Atlanta, we got lots of South Asian and Middle Eastern people there. I am assuming you mean Arab and Middle Eastern chicks in general and not women who are specifically Muslim? If specifically Muslim, convert or something bro.
Anyways, to my point, there are two kinds of Middle Eastern women.
One kind grew up around a lot of masculine men of her background and she will usually be more partial to brown guys. I find this to be true for those who are North African and more of the browner Arab. You will find that they have a lot of ethnic friends and may even have black girls as friends. From my observations, I do not see them going for a white dude unless he is really really edgy and sketchy looking. I find that even Armenian women prefer to go for a black dude than a white dude.
The other kind, you might have some luck with, grew up around more insecure men of their race. I find that Iranian and Lebanese women tend to be the most insecure of being brown and will go for a white guy out of that insecurity, it isn't nearly as bad as it is with Asian women though. If the men they are around are more of the dorky STEM type of Middle Eastern guys, you will have an easy time pulling.
All that said, they seem to be all or nothing types when it comes to white guys. You will find some that easily go for anyone that is white because they hate being brown. Others will be tougher for someone who is not brown because they take great pride in themselves.
Easiest way to gage? Tell her she looks Italian. If her face lights up, game hard. If she looks at you like you are crazy, she might be one of the proud types.
I have been with a few but typically, they are a lot tougher. I find that with hot ones, this is how they typically go for men
1. Any kind of a hot "brown" guy, usually another Arab dude that is alpha but they love Latinos and the odd Indian/Pakistani (they hate them but love them, my Indian friend slayed a lot of Arab girls, granted he was 6'2 and built)
2. White guys who can pass for Middle Eastern or are really dark (Mediterranean)
3. Black guys (some, like Armenian women, really love black dudes)
4. Asian dudes, although I am seeing a lot lately with an Asian man fetish