Re: Teacher OKs "Avoid[ing] touching females on religious grounds"
You can't just flip the details and come out with the same situation. A women-only class doesn't mean the same thing as a men-only class; refusing to touch someone because you think they are inferior doesn't mean the same thing as refusing to touch them because it's a matter of respect. Meaning and intention matter.
A class for women creates a space where women, who may feel vulnerable for many reasons, feel safe. A class for men creates a space where women are excluded. Not the same.
Refusing to train with a Jew because you think they are inferior or "the enemy" is one thing. Refusing to train with women because your religion says the way to respect women and protect yourself is by not touching them and risking lustful thoughts is quite different.
You might think both arguments are horseshit--I certainly think the second is--but I can see accommodating it if it's held sincerely and without malice.