Religion is NOT negotiable.
How about the barbaric and violent laws that many of those religions promote, are those negotiable?
I don't think it is necessarily a women not wanting to train with women issue (at least with me). It is about preference I think. I prefer to train with men, but that doesn't mean I don't like training with women.
I can understand women preferring to train with men with self defense/survival in mind because I think the very same thing.
In the long run I assume regardless of their preference they will still train with anyone and everyone. Part of Aikido is being an Uke right? IMO refusing to train with someone is failing the spirit of Aikido.
It's one thing to ask and if people accept and accommodate it that's fine. What gets me is when you hear about lawsuits popping up over it.