Hi to all,
my experience from Turkey (with a large but very moderate Muslim population
) and Belgium with a not so large but also moderate Catholic population is that no one has any problems concerning women mixing with men and bowing to O'Sensei, the teacher and your partner. Why should they? The bow is different from the bow at prayer, it's just a form of greeting or politeness in Japanese, and no one would confuse it with the bow in the Mosque.
Same for man-woman issues, and also luckily, no one thinks it should be restricted that older men train with young women or girls or vice versa. I've never observed any type of sexual harrassment in any dojo, and I don't see any sexual component in touching during techniques. If someone is looking for it, he would certainly find it, but then he would also find it in swimming pools, overcrowded buses or his office/ factory. You shouldn't restrict a sane activity because of some insane individuals.
In my opinion you could accept that someone refuses to bow or to train on Sabbath (Friday, Hindu or whatever other sacred days) everywhere in the world; it wouldn't really affect aikido - but I'd hate to train in a pure women dojo. That's just one of the main attractions of aikido - you train with old, young, male, female, heavy, light, all sorts of people. But then again, I'd refuse to go to such a country where they insist on male-female segregation or any other type of apartheid even as a tourist or for a short-time consultancy job.