Hmm... Leaving off the whole Christian ideology and other issues, I just wanted to address one aspect of this thread, namely, that of the bowing in Japanese arts.
It is religious. Deal with it.
To be clear, I'm talking specifically about things like the bowing to the founder/kamiza/kamidana/shomen at the beginning and end of class, more than bowing to partners before and after training, although the influence there is something that should always be considered as well. But that initial bow? It's a Shinto ritual. Whether or not your dojo points that out, makes a big deal about it, mentions it at all, or is even in any real way aware of it, it is a Shinto ritual. Hell, the dojo's structure is based (largely) on Shinto shrines or temples... the word "dojo" itself comes from Buddhism... and many martial traditions have their origins centred in Buddhist Temples or Shinto Shrines, with deep historical, geographical, philosophical, and spiritual connections to these religious forms.
Obviously, this is something that has it's origins in older arts... however, the basic ideas, forms, structures, rituals, and more are just as present in modern arts... Judo and Aikido classes begin with a bow towards the front of the dojo, commonly with a picture of Kano or Ueshiba, or perhaps a senior founder of the line you're studying... this is a Shinto bow. It is showing respect for those that have come before you, yeah... but that's pretty much a core aspect of Shinto in the first place. Sometimes you'll see a few claps between two bows... which is designed to both scare off potentially ill-intended spirits, and awaken protective ones... very much Shinto. If there's a small model building at the front of the dojo, that's a kamidana... a house for spirits. The front of the dojo is called the kamiza... where the spirits sit.
What all of this means is that, if you don't attribute any religious aspects to the building, the activities engaged in, the rituals, and so on, you're denying much of why what you're doing is there in the first place... you're, essentially, ignoring large parts of what you do... which leads to you missing many of the lessons and their reasons. Can you do that? Sure... but it's like learning to play tennis by only limiting yourself to forehand lobs, and ignoring where the lines are on the court... sure, you'll have fun hitting a ball around, but are you really playing tennis? Or just hitting a ball with a racquet?
As a result, I'm completely with Paul when he said he told the guy who came along that he'd never make him do anything that went against his religious beliefs as he walked him out the door... I'd do the same thing. From my perspective, and I'd suggest probably Paul's as well, if you're not going to do the thing, don't do the thing. Additionally, if your religion forbids something, then you can't do it... unless you want to go against your religion. And that's a spiritual choice the person needs to make for themselves. But to say "well, we don't think of it as a religious action" is kinda irrelevant... you may class yourself as a vegetarian, but when you're eating steak, not thinking of it as once being a cow doesn't change what it is.
Thing is, from a Japanese religious perspective, there's no conflict having multiple religious influences and beliefs... you can follow Shinto practices, attend a Buddhist temple, embrace Taoism (another influence on the dojo that adds more layers to things), and, from a Japanese perspective, also be a Christian. It's really only the Western religions that turn around and, essentially, say "my way only"... even when the difference is minimalist, only the one form that's being followed by the person in question is the "right" one... so the restriction will come from the Western religious side of things.
Of course, this whole idea of "Christian Karate" or similar strikes me as highly amusing... as the idea is often to have a martial art that is devoid of Eastern religious ideals and concepts... but are universally done by people with such a lack of insight into such concepts that they don't even know what is or is not influenced by, or are outright Eastern religious aspects and concepts there in the first place. The only safe way to not have any Japanese religious aspect is simply... do boxing. If you're doing karate, or anything similar and based in such systems, then the simple fact is, you're engaging in Japanese religious practices... even when you don't know you are.
