I am aware of the purpose of bowing in the martial arts. As you said, its a polite gesture nothing more. Bowing is more or less much like a handshake in how it is used. But, there are people who do think its a religious ritual. There are people who think that just about anything foreign or of another culture is religious. I know of a case of an instructor who used to require students to know the Japanese words for the techniques but he stopped doing that because some of the parents of the children who he was teaching were getting concerned in that they thought he was teaching a religion when in fact he wasn't, he was teaching a sport that was from a different culture but since the parents were getting concerned and thought it had religious overtones since he was requiring students to know the Japanese words for the techniques he stopped requiring that.
These will be the same people most likely who stalk me to convert.
I wonder what they think of fencing and dressage riding where a lot of terms are in French lol.