So if someone came to me and told me that due to their religion they could not bow as prescribed, or would not practice with a woman - because it was against their religious values. I would tell them that I respected them - but their religious values were against my values - both personal and religious - and so they would not be welcome to study with me.
I don't quite understand how someone's personal choice not to bow, but perhaps to show some other sign of respect to the dojo, violates your values. You express respect by bowing, they may express it with a Kung-Fu style hand push or something similar. Is it really that big of a deal?
I enjoyed reading the story about your mother. Thank you sharing that. It does leave me wondering how you can hold the position you do in light of your mom's experience. Imagine if the principal of the school told your mom, "my way or the highway." Your mother would have been expelled, probably would not have gone to college, and her life could have been very different - presumably for the worse. What good would that have done anyone? It certainly would not have made her respect the school or bishop any more - probably a whole lot less.
Yes, it's your legal right to refuse to accomodate those whose values are different than yours. Just as it would have been the school's legal right to expel your mother at the time. This is not a question of what is legal but rather what is the greater good.
How many people would have missed out on the benefits of Aikido training had O Sensei required them to convert to the Omoto faith in order to study the art?