No replies from Unitarian Universalists yet. I'll go ahead and offer my perspective.
While I don't know that polyamory would ever work for me, I understand that humans have the capacity to love more than one person, and I can't ever think that is wrong. If a couple decide a polyamorous family structure works for them, who am I to say that is wrong? From what I have been reading, some families have had this structure for years. I see no reason that polyamorous families should not be just as welcome in Unitarian Universalist congregations as members and ministers (if qualified and the congregation desides to hire them) as anyone else.
Ideally, I would think it should be acceptable to marry multiple partners, though I'm not really sure how that would work. I could see how it could get very complicated. I will leave it to others to decide how that could be worked out. Contracts, perhaps?
In reading a blog in which Unitarian Universalists were discussing the matter, I was very shocked to see the reasoning motivating those who had a strongly negative emotional reaction. One argument was that polyamory rejects the "wisdom" of hundreds of years of Western history. Using that argument, one could argue against same-sex marriage. Same-sex marriage has only been legalized recently in the known history of the entire world. The argument went on that the difference is that gay people are born gay, but we are also born with the capacity to love others, and nature never programmed monogamy into us. Having more than one partner to which one relates intimately is just as natural as homosexuality, or heterosexuality, for that matter.
Another in the blog compared it to beastiality, yet again an argument used by homophobic people. It amazes me that anyone would ever think to compare loving relationships to beastiality.
Others described it as "socially outrageous" and an "anything goes" kind of lifestyle. In some places, a same-sex couple walking down the street can be considered to be engaging in socially outrageous behavior just because they are holding hands. Polyamory isn't an "anything goes" kind of family structure so long as the family maintains consent, integrity, honesty, love, and mutual respect.
I think some of the extreme reactions to this are coming from irrationality and deeply ingrained cultural ideas in a way similar to how some people react to homosexuality. In thinking about this, I can't see anything immoral about polyamory in and of itself. Problems polyamorous families can and do have also occur among monogamous couples. I'm sure it could get even more complicated because of the number of partners involved, and that's a good argument that polyamory is not for everyone, but it doesn't indicate that polyamory is in and of itself immoral.
Thoughts, anyone?