I find it fairly disturbing that this man is being called intolerant because he doesn't touch women. I know many orthodox Jews, and according to what they have told me, not touching someone of the opposite gender has nothing to do with treating them as someone lesser. It's because they are not your spouse/child, and so you are respecting them by not touching them.
I don't think I know any woman who would feel respected if someone told her "No, I won't train with you". Quite the opposite, actually
But leaving that aside -- the described case has been compared with other situations where people need special accommodation on the mat. Elderly afraid to take rolls, maybe a rape victim who really doesn't want to train with men, etc. Right now we have an asthmatic in class who needs to take frequent breaks. Often the special treatment for such people will be greater that with the described case. But I nevertheless I wouldn't mind, don't mind, would actually like
to have these people in the dojo, would maybe add in some extra hours to help them overcome their problems.
And that's where I see the main difference to this case. A religious doctrine against touching (non-wife) women is also a problem in the dojo context, but there is no will to overcome that problem. And that means, for me, that his beliefs and our way of training are incompatible. (Disclaimer: I'm just a kyu grade, so I can't really speak for the dojo).