To the OP:
Ignore the people who issuing blanket opinions to leave it off. If your experience was anything like mine, these activities probably took a lot of time and effort on your part. Why deny yourself the opportunity to talk to adcoms about what you gained and what you invested in them?
Also, who are we kidding here? Adcoms are probably going to realize you're Muslim from your name or other identifying info (eg, place of birth). If you don't say what positive activities you've been involved in, you give some people the opportunity to believe that either you're a "fake"/lapsed Muslim or that you are involved in activities you'd rather hide.
As someone else already said, if there is a culture of Islamophobia at a school to the extent that they refuse to interview/accept you, that's somewhere that you most likely wouldn't be happy anyway. There's no point getting into a school and then feeling like you have to hide your faith for the next four years or face hate -- it's not going to be fun.
I applied to over 40 schools and only got 4 interviews (2 acceptances so far
). Did my Islam-related activities reduce the number of interviews I got? Probably not, and considering that my gpa is well below average (ie, below the cutoffs at many places), I think my gpa reduced the number of interviews I got. At both places that I've been accepted to, we've talked about my faith and my involvement in those activities. I was really able to "connect" with my interviewers (2 white men at each place) and be confident that they would advocate for me (imagine that, white guys who would actually want a female minority student at their school
). At both schools, I had extensive discussions stemming from what I wrote about my religion. If I hadn't talked about it in my applications, I'm really not sure that I have anything else that they would have found nearly as compelling, and I probably wouldn't have been accepted to either school.
Now, of course, that's just how it worked out for me. Every person has to decide if they can handle what will inevitably come their way. Just don't be so quick to assume that your faith or ethnicity will keep you out of medical school, especially if there are other glaring weaknesses in your application.