Before I even click at a link to a Unitarian Universalist website, I know with very high probability that there is going to be a "social justice" section espousing ideological positions on a number of issues.

I suppose I should reiterate this, as it seems to be unclear: My point was not that UUs don't have a degree of "group consensus." My point was that they do not treat it as an unquestionable dogma.

That they generally have a "social values" page does not seem at all contradictory to this - the issue is whether they're willing to entertain discussion from opposing views.

In my (anecdotal) experience as someone who has actually attended UU churches, the answer has been very strongly yes. If you have actual experiences to the contrary, or have seen websites from them that seem to make it vividly clear that dissent is not tolerated, I'd be genuinely curious to see this. It's entirely possible that my experiences aren't typical, but I haven't seen any evidence to support that theory.