The argument could already be made that Christianity is entirely composed of people who don't believe in God.
Vaguely. Isn't it a fairly small and atomised religion with very little influence on politics, culture, societal norms, etc.
Unitarian Universalism just borrows from other religions (mainly Christianity) and honestly, it's a total waste of time in my book. My parents are all into it and since moving back in with them, I've gone to a few just to try and keep an open mind about things... but it's pretty much the new incarnation of Christianity .
It bears some resemblance to what the OP was talking about, a church where you can believe more or less whatever you want, without getting thrown out by right-wingers. Yeah, it's a small denomination, but it's been around a long time, and is growing in liberal, hip places like Asheville, NC.
I think you're missing the point of why I'd want to do this in the first place. If you avoid the "right-wingers", you're basically just saving them the effort of throwing you out by not turning up in the first place. Who does that help?
So...you want to join a church filled with people who hate people like you? Have you ever tried this?
People like who? I hardly think the church is "filled" with those kinds of people. They just represent a greater proportion than they did when atheism and not-giving-a-shit-ism were less societally acceptable.