Actually, most martial arts are just that: arts of war. Whatever Eastern spirituality that has been put into them is generally not central to the actual training.
A great example is Jujitsu, which originated in Japan but has spread to the world via Brazil and the Gracie family. Many of its dedicated practitioners are Brazilian Catholics. You can find Eastern philosophy in almost anything, but the raw physical training is purely physical.
Tai Chi is a bit unique in this regard because its normal practice is directly tied to Taoist philosphy, but again that is a matter of adding spiritual meanings to the movements rather than making movements out of spiritual meanings. Given its nature, however, I’d bet you’re very unlikely to find “non-denominational” Tai Chi.
On the opposite end of the spectrum you have Muay Thai, which has some spiritual trappings, but those trappings are really more equivalent to Irish boxers doing the sign of the cross before a bout. Muay Thai is the very definition of a martial art. It is designed with one purpose in mind, and that is to utterly devestate your opponent. Even the “entertainment” uses of the sport are ridiculously brutal and bloody, and an argument could be made that it violates Catholic morality not because of any Eastern spritual elements, but because its improper use is extremely deadly. I’ve watched Muay Thai fights at bars in Thailand, and even the 3-minute-limit matches almost always ended in a knockout.
