Re: more religious issues
What would happen if you go to a Muslim temple and not bow when you prayed. You stood erect with hands stretched out in the air, what would happen? There is a certain level of respect people have to understand.
A student may not bow because he is Jewish, Christian, or Muslim not bowing (to false idols) and O'Sensei may have allowed it, but that doesn't reflect upon his opinion. Bowing is a sign of respect, just as a hand shake. There allot behind a bow, a show of civility, respect, etc. In fact non-Asians, such as the English have employed bowing as a greeting and show of respect. Bowing is a not verbal communication of respect, civility, and good sportsmanship and friendship, in context to the object being bowed to. If you don't bow that agreement of behavior and attitude you are sending a message not of peace but of war.
I see bowing no different than a handshake, and in my book if you don't do either you are saying you will not respect me, be friendly, courteous, a gentlemen or a lady, etc. I don't want to train with those kind of people or have them in the dojo. They are not interested in Aikido's message of peace.