An American woman can adopt Islam without dressing in any way that identifies her as Islamic.
My bet is that almost none of them do, that the Western converts ALWAYS adopt the distinct wardrobe that identifies them.
The women get structure, rules, and a new wardrobe while also being able to see themselves as rebellious as they are escaping the chaos of being independent.
I think you are correct. I think many of them rebel against "patriarchy" BECAUSE Western men don't give them the structure, order, and security they secretly crave.
Interesting, I wonder if they have an internal ambivalence resulting from their brainwashed formal education on their frontal lobes. While they experience (what some say) a biological feminine urge to be dominated..controlled and bred by a dominant male?