If it is supposedly unconstitutional to prohibit homosexual marriage, then there is no way you can justify prohibiting polygamy or polyandry or group marriage or even incestuous marriage or prostitution (rent a marriage).
As long as one or more people “love each other”....
Frankly polygamy is historically a normal human condition. Homosexual marriage, however, is an abomination against both God and Nature.
I think if polygamy is permitted then polyandry must also be permitted.
Your point that foreign cultures have had polygamy for millenia is, I believe, factual. Also, the bible nowhere condemns polygamy. I am under the impression that Martin Luther sought, but could not find anywhere in the bible, such condemnation.
I also think Mormons, however misguided they may or may not be, were violently persecuted in the US in historical times for their historical beliefs.