I have to respectfully disagree when you state that the only person affected is person with the religious restrictions. I have had direct experience with this issue, and I must stated that the female partner is also affected in a few circumstances. First, she does not get a different person to train with - you know different body type. She has in effect one less training partner on the mat than all her male counterarts.
Second, if practicing jiyuwaza/randori and the male practitioner with religious restrictions turn is up, she must sit out because he does not want to touch a woman. She gets left out in this specific instance and he doesn't. If you train jiyuwaza a lot in your dojo this can happen a lot. Third, there are times where she can be the only woman in a very small class of three. The two males both have religious restrictions against touching females. Who gets left out? She does. Who doesn't get to train for the day? The woman.
The person with religious restrictions to training with women aren't going to be 'forced' to train with women; they'd just leave. The women in question are not going to be able to train with this religious person no matter what happens. Either he's allowed in class and trains only with men, or he doesn't come to the dojo at all. In your second case, it's not that she'd have two people to train with that she otherwise wouldn't, it's that she'd show up at the dojo alone.
You are only required to provide a REASONABLE accomodation not any accomodation. In my opinion, if any other student's practice will be adversely affected by the request then it is not reasonable.
whenever we train with other people, someone
is going to be adversely affected by someone else. Stinky Guy? He adversely affects my practice when he interrupts my ability to remain upright in kokyu-ho by breathing on me. Loud Guy? He distracts me from across the dojo with his yelling. Flirty Gal? She just annoys the heck out of me. Heaven only knows what I
do to distract or annoy other people. Opinionated Gal? Throat-punch Gal?
I think that if there's a question of training or not training, the Religious Guy should be the one to sit out, not the women of the dojo. Nor should women be forced into a females-only ghetto on one side of the mat. Let Religious Guy train, but just like Stinky Guy gets a talking-to when it gets so bad that he's doing no-touch aikido from six feet away, so should Religious Guy be limited in his impact - but if he's willing to take responsibility for that, don't just leave him on the curb. It's good for him and good for all the guys in the dojo to have another set of hands.