Yo-Jimbo

To me it isn't a big deal either way, I bow not because I'm supposed to or have to, but because I choose to respect the tradition and the others involved. I avoid doing things that I think are wrong; people have the right to govern themselves. Hopefully, when anyone bows, they know why they are doing it. Two people could be doing it right next to each other and be doing it for different reasons. Two people could be refusing to bow right next to each other for completely different reasons.
If you can't bring yourself to bow for any reason within your conscience, please don't abandon aikido over it (typical aikido practice spends little time doing it and little hinges on it). Perhaps, some will interpret not bowing as disrespectful or closed minded, but that should only matter if it is being done to impress someone with how virtuous one is instead of placating whatever Power(s) one consigns.
Yet, I would throw out the following (which I hope would bring this eternal debate some resolution). What would you do if I told you that *insert other faith than your own here* did *insert common activity here* as a way of worship? If someone worships the Green Mother by sitting down in a chair and eating food, communes with the 8th plane by sleeping on their side or shows their respect to the inner beast by defecation (a strange sort of deification), are you ready to stop doing all these things? These are all things you can't avoid you say. These are all hypothetical you say (although I made them up, I wouldn't be surprised if people somewhere did all of these). I have to sleep, but I don't have to bow. OK, well, some Baptists have been known to do submersion in water as a form of worship (I think they call it by the same name that we Catholics do, baptism). Anyway, I'd like to see the hands of everyone that is now ready to give up bathing and swimming so that no one will think that they've gone Baptist (or Catholic, or whatever).
I guess it has always seemed to be just another of our very human hypocrisies to me. Then again if your religion/personal belief has very specific verbiage on this subject, I suggest you continue to do whatever will protect your soul/karma and not bother with permission from any other authority than the one it belongs. We humans may even achieve great things if we can just figure out to whom that authority really belongs.
Although I am trying to sound sanctimonious, I'm sure God will continue to keep me in my place (most likely by ignoring me as the insignificant nuisance I am). Though I am not worthy of wiping the dust from anyone's feet, I would still try to lift everyone upon my shoulders.