You left out the next line about having respect for the environment you're in and that's the key. I wouldn't expect anything to happen to a person visiting a mosque and not praying the first time, but I don't think the individual would be welcome there more than once if he continued with that behavior. Of course I don't understand why one would visit someone else's house of worship and then try to maintain his own religious practices there.
There are rules in every organization that must be followed to be a part of that group. I can't enter the Morman Temple in Salt Lake City and I can't visit the holy city of Mecca since I don't follow either faith. While I'd like to do both, I'm not willing to convert to either religion for the privilege. I'm not offended and don't feel that I'm being discriminated against. I'm sure that I would be welcome if I were willing to convert. This isn't the same as the dojo situation that started this thread, but awfully similar in nature.
We bow to each other, we train with everyone present without regard to their sex, their sexual orientation, their race, their national origin, their politics, or their religion. Heck, we'll even train with BJJ guys - and you know how THEY are. Seriously, we are inclusive and if you don't wish to share that inclusive spirit, train somewhere more to your liking. We don't have to be disagreeable or antagonistic.
I can respect your opinion, but why is this subject such a big deal? Accomodating someone's religious preferences is not the same as changing the rules just for that one person. It really is not that big of a deal. And it really is something that is not hard to do.