Thanks for all the replies! Based on what I've read here, and in other places I decided to start an Aikido class. I'm really looking forward to it, and I think that many times people in the church have preconceptions about a particular activity, and they think it must be wrong.
It may be because that is what they were taught, and they didn't actually research it themselves. So I decided to start, and make a decision based on this first (beginner) training class. From what I have seen and read though, I don't think that there is a conflict of interest between what I believe and what Aikido teaches.