WOW, I am deeply sorry for whatever you thought I said or position you thought I represent.
And I'm sorry if I upset you. To be honest, you said some things that I find quite problematic, not in their intent but in their implications. I think I understand what you're trying to say, that you would like everyone to get along, and you would hope that over time a new student's attitudes would adjust. But you've also talked about legal rights, and as I pointed out, we can't just manufacture different legal rights because we think that's the way things should be.
I've been using the lunch counter analogy, but here's another one: a bar/restaurant. Observant Muslims do not drink alcohol and eat only halal food, and no law in the US compels them to do otherwise. Likewise, the law does not demand all restaurants to be alcohol-free and serve only halal food. If a Muslim chooses to walk into a restaurant that serves alcohol and does not serve exclusively halal food, he/she has no legal right to demand a cessation of alcohol-serving and an all-halal menu.
So what's the solution? We have to accept that there may not be one -- not a mutually-agreeable one. For that, you need flexibility and room to move, and you may not have that. Depending on the composition of the dojo and the nature of the training, insisting on only male partners may indeed deprive female members. Certain Muslims may feel that their beliefs do not permit them to bow to their partners or toward the kamiza: however sincere the belief, on the face of it, this is no more legitimate and should carry no more weight than the belief of a sensei or their partners that not bowing is disrespectful. If there isn't some room to move, there is no solution -- and if one side is rigid and unwilling to move at all, I think it's really unfair to put all the blame on the other side for not being willing (or able) to move far enough. A restaurant owner can't shut down their business because it cannot possibly accommodate the "need" for it to be alcohol-free and totally halal. They can offer non-alcoholic beverages, and part of their menu is almost certainly halal already with no changes made -- if you, as a Muslim, are ok with that, then you're all good. Or the restaurant could add additional offerings to give more offerings to Muslims, which of course non-Muslims would not have a problem with either. But a woman can't stop being a woman.