Re: When you bow do you worship or just...
Part of respecting other people's cultures is respecting their right to opt out of certain rituals; it works both ways. I can't really imagine that someone who has chosen to practice the 'Art of Peace' could be offended by someone else choosing to prioritise their religious beliefs above certain aspects of their martial training. Declining to bow out of deference to a religious belief is not disrespectful to Aikido or its founder; it is simply being respectful to one's own religion, which is perfectly consistent with Aikido's philosophy - it does not require from anyone that give up their religion and become a Shintoist or anything else.
Here in Morocco, everyone I train with is Muslim except our Sensei who is Japanese. We do not perform the full seated bow (which brings the forehead almost to the ground) because this is part of our prayer, which we reserve for God. Instead, we perform a kind of 'half-bow', leaning forward on our hands slightly. When standing, we bow to our partners in the normal way (Islamic bowing is much deeper, with the back at a right angle with the legs, so there's no issue). Our Sensei, being Japanese, bows (when sitting) in the usual Japanese way, and has no problem with our bows being different from his. This is a reflection of the tolerant culture from which he comes. It is not intolerance which prevents us from bowing exactly as he does, but rather religious conviction. Intolerance would be for us to prevent him from following his own religion and customs. It is not intolerant to make a personal choice; rather intolerance is preventing someone else from doing so.
Our Sensei, when greeting us off the mat, shakes our hands and says 'salam aleikum'. Nobody asked him to do it; he is simply trying to join in with the traditions of the country in which he is living. It cannot be said: 'if he joins in with your traditions, why do you not join in with his?', because shaking hands and saying the salam is not an intrinsic part of Shintoism, to be offered only as a religious act of worship, never to a human being. It is not a part of Japanese culture at all, one way or another. As for the full bow, it crosses over into both cultures, Japanese and Islamic, and therefore has deep meaning in both. Representatives of each of these cultures should be allowed to act in accordance with this without being accused of being disrespectful.
To attempt to make further analogy, and suggest that 'if bowing is left, surely the dojo, the gi, the hakama, the terminology etc must be left too', is illogical. Why? Because these other elements are purely Japanese, there is no shared culture which could lead to problems of this nature. The bow is not particular to Japan; it has Judeo-Christian-Islamic connotations and significance, and therefore there must be allowances made for people of those traditions to adhere to their cultures' interpretation of it. This is not disrespectful; rather, the opposite. It shows respect for the culture one has chosen to explore without compromising one's own deeply-held beliefs. This is a basic human right which I do not believe O-Sensei, or any other man of intellect, would expect anyone to forfeit.