There is a truly fabulous discussion of polyamory going on at The Lively Tradition.
A few thoughts.
I talked about my feelings on polamory here
Essentially, I don't particularly have a problem with it when it is practised unselfishly. I'm not entirely certain a family with kids CAN practice it unselfishly, though I suppose that if people who had been in a stable relationship for some time had children and were committed to remaining stable, that could work. Polyamory does not strike me as sufficient grounds for removal by child protective services, at the same time, I don't know that most people are up to the challenges of balancing their needs with their lovers' needs with their children's needs.
My understanding of the sociology of polygyny (one man with lots of women, polyandry, the reverse, is unusual almost to the point of being unheard of) is that it has traditionally been practiced in societies with great weath disparities under the theory that women consider themselves better off the tenth wife of the king than the only wife of a peasant.
(Note also how the extramarital affair is really common among powerful men and how woman often chase powerful men and do their best to seduce them into that sort of interaction.)
Anyway, I really hope polyamory isn't the root of the IA mess.
It's not my favorite choice and I think it is best practiced as a private thing, but I would certainly not object to polyamorous folks being active members of my church.
At the same time, I am really wary of getting dragged in to another political struggle that I only semi agree with.