Expect the Christian fundamentalists to use the quasi cultural/religious 'modesty' of Muslim women as a propaganda tactic against women's independence in the United States. Christian, Moslem and Mormon fundamentalists will gang up to impose their shared desire to strip women of all rights and enforce their control over women's bodies and behavior just as we have already witnessed the combined efforts of the ultra right Christian and Mormon fundamentalists combine to lie and scheme to defeat Proposition 8 in California.
As for the segregated bathhouse, well, all precedents seem harmless in the beginning ...
This all makes me uneasy. I'd be much more comfortable if these differences in dress and behavior were attributed to culture and diverse cultures respected in all reasonable aspects. When religion gets involved then the first step is for the minority religion to demand its right to their own specific version of their cultural preferences (which of course come from their own version or God). All fine and good. But once those have been accepted the next step is to suggest, then demand, that everyone else should follow their rules, because, you know, their rules are the right ones, obviously. Their god said so.
How do we keep them in the 'live and let live' stage? The US Constitution was supposed to help with that. But with everyone ignoring it lately it has not counted for much.