Religion is a spiritual belief. For a few martial arts, a martial art is also a spiritual belief. I believe that the martial arts are simply physical ways to manifest a warrior spirit, which has nothing to do with spirituality. It is merely the way a warrior lives and behaves in the combative society that humans have created. A religion may practice a martial art or a martial art may be connected to and/or worship a religion but that does not mean all martial arts have connection with a religion. Some, if not most, martial arts have no religious connection.
Physical things may be explained through the scientific method, but spiritual things cannot, and have not, been proved scientifically. Religious proof comes from anecdotal evidence, which does not really prove anything; it just people recounting what they believe they have experienced. People will believe what they want to believe not matter the logic, reason, or evidence to the contrary. The purpose for, and use of, bowing falls under the category of something that people will believe what they want to believe.
What is bowing? As a physical act, it is simply bending forward at the waist. Is the act of bending forward at the waist a sin if it is done for any other reason than to worship God? Which does the Bible condemn: the physical act of bowing or bowing in worship of another god?
In your Christian religious services, do you bow to God? Probably not! In Western Christian religious services, we do not use bowing; we usually prefer to kneel before God. In Western Christianity, bowing is considered archaic.