What are your thoughts on this?
That's a good question.
How does your question apply to Christians?
I'll offer principles that you can apply to martial arts or any other endeavor.
A. If something involves an unbiblical practice, don't practice it.
Example would be Yoga. It is an essential Hindu practice. Some say they just do it to stretch. However, that's like going to a mosque to sing and chant the Koran to develop on vocal skills.
I bring this up because there are writers like Constance Cumbey who spread disinformation, equating Yoga with martial arts. Those writers pose as experts in a given field, but when challenged seem as if they have disregarded God's Word for philosophy and vain deceit.
B. People tend to integrate their philosophy and religion into things they are devoted to.
Some even do this with sciences and medicine. That doesn't make all science a false religious practice. However, some science so called, should be avoided.
Are there martial arts that integrate false religious teachings?
Of course there are. Most martial arts taught in USA are from the orient. Many of their teachers immigrated, bringing their religious views with them. That is why believers in Jesus Christ are forbidden to engage in unbiblical practices. I would not even take classes from someone calling themselves a Christian, who taught some unholy philosophy in their classes. However, there really are those who teach combat, self defense, martial arts who do not spread eastern religion or occultic practices. Many teenagers will sit for hours in front of video games going through simulated magic without parental direction. I've talked to parents about how their children should not read the Harry Potty series or Book of the Dead. That does not mean we are against reading. However, the excuse I hear is that their children are engaged in the healthy practice of reading. That is why it's up to the parents and pastors to direct, train in the Word, preach, provide discernment and proper boundaries.
C. There are many examples of martial arts in the Bible. They are skill sets that can be used for good or evil.
I can prove that God approves of his servants training to develop skills that are used for His will.