You know I'm a big believer in the power of a good idea. What bugs me more so than anything else isn't the quality of performance, or the puppets but (from what I've seen) the lack of ideas.
Maybe I'm making huge generalizations here, but quoting scripture and telling bible stories can be done by anyone. I think that Christians (or members of any other religion for that matter) who want to use puppetry as an aspect of their faith should use it as a medium of self-expression. Don't rely on stock puppets and generic scripts, use puppetry to tell me something. Talk to me. Communicate your ideas, beliefs, values and why they're important to you as a member of your religion. Use puppetry to start a discussion and build a bridge between your community and others.
I think there's few, if any, groups doing that right now because it's hard. It's not the money, the skill or expertise that's the problem. It takes a lot of work, thought, creativity, and (dare I say it) faith.
It's much easier to just hit like-minded people over the head with a big, fat dogmatic club.