I basically agree with you so I’ll leave off adding corrections like cops don’t “investigate” rape…
Sam Ursu

There are two separate answers. The reason that women face more misogyny in America goes back to our roots in Puritanism in the same way that this countries insistence that the poor deserve to be poor is rooted in the Protestant Work Ethic. This countries entire value system is derived from those early settlers. Often people talk about how this country was settled by people looking for relief from religious persecution, and they are right. What they forget is that the religion hitting our shores was far more restrictive, especially when it came to social morals. Fast forward to now and the influence spreads past our view that women are somehow dirty, wrong, deceitful, etc. It goes beyond our reluctance to have women leading us, we also demand some kind of adherence to “family values” in our leaders. Look to France… They have had leaders with mistresses, leaders who got divorced and remarried (to singers from another country no less) during their time in office with no dip in popular support. Try to imagine that happening here! No. Here you have to be married to a modest quiet woman. Both of you have to go to church, wear your flag pins, and raise your 2.5 children to be acceptable as “moral”.

Now, as to the Muslim ability to have women leading them — that gets into complex issues of benevolent sexism but the Muslim culture actually reveres women highly, that just leads to actions that the west cannot understand (and some actions that are often detrimental to the daily lives of women, don’t get me wrong) so it is easy for them to accept a female leader when even the homes have matriarchal elements.