I can respect your opinion, but why is this subject such a big deal?
It's a big deal when (as in the example that began this thread) accommodating someone's religious beliefs means denying access to another student. If you step onto the mat, you must train with all students, not just students of your gender. If you refuse to train with students of the opposite gender, and that refusal is accommodated, you are depriving those students of practice partners, others as well as yourself.
Use a simple example: Bob wants to join a dojo. Because of his religious beliefs, Bob will not train with women. He steps onto the mat with Jeff, Steve and Ann. Not only can Ann not train with Bob, but she also is deprived of practicing with whoever Bob is paired up with because he "needs" this special accommodation. If the class consists only of Bob, Jeff and Ann, what then? Jeff is okay training with everyone. Ann is okay training with everyone. Bob insists that he will only train with Jeff. Should Ann have to sit out so that Bob's beliefs can be accommodated?
Insisting on accommodations like this is the kind of big-elbows, "you're not letting me practice my religion" behavior that gives religion a truly deserved bad name.