In response to Hafidha's comment...
1. Politely start asking questions.
Do we really need it?
Can we point to any recent successes other than small amounts of publicity? (And I do mean small. According to Google news, the only publications that even noticed the "Quickly abandon Iraq and watch the Iraqis who trusted us get butchered" petitions were UU World and Bay Windows.)
How much does it cost?
Do the resources we spend on it really do anything other than make us feel good about ourselves? What could, say, Beacon House do with those resources?
Is it projecting the public image we want to project?
Is it truly representative of who we are as a denomination?
2. Talk up the issue among UUs and get them at least thinking about it if not talking about it themselves. You would be surprised at the number of UUs who have never even considered the issue of being welcoming to conservatives and moderates or how it must feel to have liberal statements made constantly on your behalf when you don't agree. Such people are usually pretty understanding when you actually explain the issue, but it just isn't something that occurs to most UUs.
3. Suck it up. Because UUs, particularly the sort who go to GA, are way too in love with the UUAWO to get rid of it, and nobody in the UUA cares what the moderates and conservatives think any more than the any elected officials actually care what the UUs think.
4. Pause to appreciate the irony of #3. Then go back to 1 and 2, keep thinking and keep talking and wait for the time when our voices make more of a difference. Because UUism is flawed, but is full of good people and is well worth sticking with and fixing.