I've wondered what others have thought about this topic. I believe this is why I studied under the Tomiki-style as opposed to most of the others. For myself, having gone to a few Ueshiba (traditional) classes in college, something seemed awkward with bowing to a portrait of Ueshiba. It was one thing to respect the 'living' instructors, but I couldn't wrap my mind around this particular tradition. Oh well. (I guess I should note that I was just below a black-belt in the Tomiki system prior to college).
As a Christian, I was interested in Aikido because I didn't need to 'break' anything, and that I really had no way to use the art except if I happened to be attacked. It also helped me get over my fear of falling :-)
As for the benefits of martial arts, more churches are using them as ourtreaches to the community. The Christian church I currently attend--a non-denominational evangelical one--actually holds martial arts classes on the premises. However, I should note that this pretty much sticks to technique, fitness, self-discipline, and women's self-defense.
I think the concern of some churches (perhaps most) is of some of the meditative aspects of certain arts. If the goal of meditation is to 'empty' oneself of 'whatever', then something has to fill that void. Anyway, as my pastor would say, not a sermon just a thought.