Re: more religious issues
I think if the "excluded" people started already a campaign against the dojo via their temples, that is pretty strong. They are not excluded because of being strict Moslem/ Jew/ evangelical Christian (or whoever refuses training with the opposite sex) but because of upsetting aikido training rules, which is a strictly technical issue.
In my dojo we once had some boys refusing to train with the girls. Not because they were religious, just because they had the age when girls are absolutely unworthy, ridiculous, feeble creatures whom a REAL BOY doesn't want to mix with. Obviously they had to leave the tatami when showing this attitude. So if they are sent away but other boys refusing girls for religious reasons are admitted, who would be discriminated? The non-religious-anti-girl boys, or the girls? I think if a dojo is pretty straightforward postulating that everyone trains with whoever bows to him, then no exceptions should be made, be it for personal dislike reasons, religious reasons, technical reasons (X is such a bad uke!) etc.
But on the other hand, as already someone wrote, no one prevents people who are uncomfortable to train with the opposite sex to set up a strictly purdah dojo. In Turkey, most Turkish baths are gender separated, everyone knows, and it's a problem for no one. But on the other hand, no one would issue a fatwa against a Turkish bath were mixed bathing hours are allowed - but conservative or very religious people just wouldn't go there.
(who would hate NOT to train with men and would do my best not to be confined to an all-women.dojo....although it might be fun to try that once or twice)