We had a woman who told us she didn't want her son to bow to the flags because "that's idol worship". I explained that it was a coutesy. A sign of respect. Akin to shaking hands or saluting the flag in a parade. And that such respect is required. She didn't bring him back.
I feel sorry for the kid.
I understand that is a belief of the Jehovah's Witnesses, along with not serving the the military of their country, nor accepting blood transfusions.
I also understand that Zen is a variation of Buddhism, and that it was incorporated into the study of some of the martial arts. Aikidoists that I have seen always bow to the picture of their founder before and at the close of class; which might be viewed as more than a simple custom in many people's eyes.
Understand that most if not all major religions are exclusive. That is, they do not accept any the practice of any other religion as possibly co-existent with their own. Further, they understand many practices of other religions are in violation of their own beliefs.
In the Christianity of the Bible, one must follow the teachings of the Bible. There is no other belief system that can provide salvation. Anything that is not of God is necessarily of Satan. In Christianity, and many other religions it seems, it can be no other way. With that in mind, go back and read Tony Dismukes post above. Agree or disagree, it may at least provide some insight.
The post given by the OP, looks very close to some of the same things in Larson's New Book of Cults, reference martial arts. FWIW, I don't personally agree that a MA is a cult just because it is an MA. Some MA may be, but it doesn't mean all are. Back in the mid-60s, Jhoon Goo Rhee was a member of the Unification (Moonie) Church, which is generally considered a cult. He in no way tried to proselytize his students, in fact was quite reluctant to do so if asked. He was a very excellent teacher of TKD, but not a proselytizer of his religion. What he is or isn't now I don't know.
My GM in the Hapkido I studied was a Christian, specifically a Baptist. He was an incredible teacher of Hapkido. Religion never came into his teaching, even remotely, other than a time or two when he and I were doing something not related to either Hapkido or religion, he might break into a hymn. We were expected to bow to the flag and to the dojang on entering. It was a sign of respect on the same order as a salute or handshake. Nothing religious about it. We would bow to the teacher and other students at appropriate times, again like a salute or handshake. If it had been otherwise, I would not have done it. I suspect many people here at MT would feel the same.
I guess my point is to say I don't agree all MA are religious cults. Larson and others seem to believe so. That is their prerogative. I don't happen to believe as they do, and I suspect they are reading things into what they may have seen or heard, but without real understanding. And to answer the OP, no, I am not put off in any way. There are many people who are ignorant about many things. Mostly their beliefs don't affect me, so why take it personally.
EDIT: I meant to add that your title is rather sensationalist. There is no mention of witchcraft in what you quoted.