Well to be honest Christianity shouldn't be viewed on our cultural norms. It doesn't explicitly say no to polygamy other than some advice from Paul saying you *SHOULD* have only one wife if you're looking to be in places of leadership within the church. The thought process is that you will be too busy managing your own life that you won't be effective in your church role. Well you shouldn't practice polygamy in many places of the USA because it's prohibited afaik. I honestly haven't looked at the laws concerning it very hard.
Historically polygamy is illegal in the USA across the board—even in Utah. Conflicts over polygamy was a basis for persecution of Mormons and the LDS church.
As for recent changes in US law, about being able to marry who you love, we're not there yet and may never legalize forms of polyamory. Civil marriage is still viewed as a contract between two consenting adults (with family involvement in cases where a partner is legally underage). Church marriages remain governed by religious doctrine, procedures and custom. Although I presided at weddings/hand-fastings for several couples, only once did I sign the marriage certificate. All the other times the couples either had another ceremony that was binding under civil law, or not because that wasn't available for same-sex couples at the time.