I don't like groups like this. It's not the religion part that gets me, it's the "overboard paranoid" assumptions that bother me. For example, straight from their website:
Karate - Martial Arts - Christian Martial Artists - Martial Artists for Christ
2. Be wary of a class that emphasizes meditation and breathing exercises.
3. Avoid instructors who claim to be able to teach "spiritual" principles like chi or ki and "internal powers.
4. You don't have to take lessons from only Christian instructors if you feel comfortable that your teacher takes a purely, "secular" approach, but you might want to share your own faith with him.
There nothing wrong with meditation and breathing exercises. There are 1000 reasons why someone would meditate and do breathing exercises. If a person expects to have better control over their body then they will need some sort of meditation and breathing exercises. Just because there is meditation and breathing exercises doesn't mean that there's a religious connection to it, especially when it comes to any thing that requires demanding physical activity.
Avoid instructors who claim to be able to teach "spiritual" principles like chi or ki and "internal powers" Ok here are 3 different things that aren't related. Chi is not a spiritual principle. Learning to manipulate the energy in one's body is no different from people who have learn to increase or decrease their heart rate at will. Or how some people are able to control how their body copes with pain. Internal powers I can understand because there are people who make it seem as if they can fight off 20 people all at once with some magical force or supernatural power.