An entire medieval Muslim populace did actually accept rule by a woman, on at least two occasions that I know of (among major states), though one was very short-lived because too many powerful neighbours refused to accept it. More recently, a number of major Muslim countries (Pakistan, Turkey, Indonesia) have been governed by women, whereas plenty of Western democracies like the US, France, Belgium, the Netherlands, and so on, have not. Of course, in all but one of those cases, the woman in question was the wife or daughter of a former male ruler, rather than having an independent power base, but then that would also have been the case with Jasmine.

Next, blaming FGM on Islam is utter nonsense and I'm quite sure you know that very well. In a country like Egypt, it is or until very recently was near-universal among all religions, having started at some undetermined point in the Greco-Roman era (if not even earlier), long before Islam came. Same in the other parts of the world where it's practiced a lot, like West-Africa: it's common among Christians, Muslims and animists alike. And there are plenty of Muslim countries, some of them with far stricter Islamic laws than the relatively secular Egypt, where it's rare or almost unheard of.

And while I'm at it, it's only tangentially related to this topic but I've been wanting to mention it to you: your comment about the harem reminded me of Massie's biography of Peter the Great that I'm finally reading, and how shocked I was when reading about the 'terem' as it existed before Peter's time. Obviously it's not a direct equivalent, but still, in that era, an Ottoman or Safavid princess could clearly have a freer life with more autonomy and potentially political influence than a Russian one, until Sophia came and rewrote the rules. The book in general is definitely worth the praise I've heard from you and others, I'm only at the Battle of Narva but already I'd consider it one of the most fascinating history books I've ever read.