As far as the Shibata kyudo group in San Francisco/Berkeley goes, the only way that Shambhala is directly part of the class is that we rent space from them in Berkeley (in SF, we use space in the (Shinto) Konko church) and the class gets a mention in their pamphlets. I do not believe that any of the currently active members of the dojo are involved with Shambhala, although some practice Zen. There has never been any sense in the dojo of being part of their organization or being "recruited" (nor would such overtures be well received). None of their ideas (or tantric theories) are present the beginner's level that I have been exposed to. Shibata emphasizes that kyudo is "moving meditiation," but I have never heard anything more esoteric. I have, however, heard all the technical principles that Earl just mentioned.
All or our classes do start with 20 minutes of meditation (with a bell to mark the start and finish). We then do fairly standard bowing at the altar (with a picture of Shibata sensei on it) and the teacher. The bowing is nothing that would seem out of place in an Aikido dojo, but I can see where the Shambhala tapestries, pictures, and whatnot in the room could make it seem more religious than it is. Certainly the class I usually go to, in a concrete basement of the Konko church, doesn't seem religious at all unless you feel that meditation is inherently so.
I've also been to classes at the New York dojo, and the situation seemed similar. My impression is that while the organization started very tight with Shambhala, as it has grown larger it has diversified along with the different instructors. However, I have not been to any of the large National seminars and have only met Shibata once, so I really can't speak much about what goes on outside of Lucy's dojo. Certainly I'm not somebody who has any standing to speak for the organization. For official background read http://www.zenko.org/about.html
Any more senior members of the organization who frequent this board would currently be off at the "Zen Mt." seminar. Perhaps some of them will have more insight (or corrections) to add when they return.
To summarize: it what I have experienced in our dojo, neither Shambhala nor any other religion is central to our practice—meditation is central but non-sectarian. I would expect that some people have used this kyudo as a stepping stone to Buddhism, and we have had Zen practitioners take up the bow, but at least in the kyudo I have seen, religion and practice are not intertwined.
Spencer Burns
<a href="http://www.yachigusaryu.com/">Yachigusa-Ryu Aiki-Bugei</a>
San Francisco, CA