I am concerned that they will treat supernatural claims as reasonable. I consider myself rational enough to be able to put up with some of the crazy stuff many UU individuals believe (beliefs not shared by the community). I am worried that my children might believe them, and even more worried that might not look at beliefs critically enough.
Yes, they will treat supernatural claims as reasonable, and expect you (and your kids) to treat them that way as well, at least in public, and condemn you (and your kids) for being rude if you (they) don't.
If you live in the United States, the odds are high that your child's school will do the same thing.
My suggestion would be that you teach your children how to operate sensibly in such an environment, rather than try to keep them out of such environments, but of course parenting advice from strangers on the Internet is pretty much worthless.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.