One of my Aunts asked me some questions about martial arts. I perceive they may be relevant to others so I'm posting them here. (I attempted to modify my words so they applied in general instead of to a specific person, if I missed something feel free to post in the comments.)
As far as beliefs go a martial arts style could be anywhere on the map. You can ask at the studio if they have any informational papers concerning their beliefs (I know that my studio has several.) However, in my fifteen years of martial arts experience - as both a student, competitor, and instructor of martial arts - I have never run across a style that inherently opposes Christian doctrine. That being said, I have had students over the years who definitely had an Un-christian experience while training. Here are my thoughts:
1.) I would not recommend a style that emphasizes the fighting aspect of martial arts. First, it is the least useful of the skills you will learn*(see footnote) and second of all I feel that many physically dangerous and psychologically negative experiences come from fighting (also known as sparring). Instead I would look for a style that focuses on kata, self defense sets, and what my instructor calls "The Pillars of Martial Arts" (those being Knowledge, Skill, and Attitude.)
2.) A studio should not stress private lessons. They are usually a method of getting more money and remove the safety found in being in a group. Ideally class sizes should range from 5-15 students and should be divided by age (for both easier learning and increased safety). My studio tries to keep a ratio of 1 instructor and an additional assistant for every 5 students.
3.) Chances are, if a doctrine comes up in karate that seems contrary to Christian beliefs it is an opportunity for discussion and probably not a reason to quite training. Keep in mind that Japan has a different set of social customs than we do and something that might seem inappropriate to us could have a very good moral basis. For example, a good friend of mine who trained in guardian Kenpo (which is a Christian style of Kendo that purposefully excludes bowing) once asked how I could justify bowing to my instructors and fellow students when the bible clearly says that only God is to be worshiped. I replied that if I thought that I was honoring the individual as an end every time I bowed to then it would certainly be a wrong thing to do. However, we explain to each student that what we mean by our bow is that we are agreeing to train together, and do not will each other harm.
In short: I doubt that anything fundamentally contrary will come up in a persons training. Still, discussing the basis for any questionable activities or beliefs will be both beneficial to him and a good way to keep you informed on whats happening. (this applies to those with children, adults can decide on there own if a practice seems reasonable.)
4.) Lastly, I URGE you to google the name of your intended instructor, the name of the studio, the address of the studio, ask people in the area and other students what there experiences are like and in general to look into it as much as is possible. There is nothing sneaky about trying to learn the background of your instructor. If you persist in training you will form a very strong bond with both fellow students and instructors. I would not hesitate to say that two of my karate instructors are on the top five list of the most formative people in my life.
* An emphasis on fighting is mostly harmful to younger students. Really any form of training will help them in a pinch and a focus on competitive an physically challenging fights is dangerous and not that helpful. Keep in mind that situational self defense is, at its core, an attempt not to fight, and therefore does not group with standard fighting practices. No style is a practical art in my mind until it does cover situational self defense. That is: how to avoid a fight, how to get out of a fight, and if need be, what your priorities, legal obligations and best chance for surviving if you get in a fight are.