Are you concerned about communities that will primarily practice polygyny? The social implications are pretty horrific for those communities.
The communities that practice polygyny are doing it right now, regardless of the law. It can be pretty brutal, but so can monogamous marriages, and they should be treated the same. Domestic violence should be (and is) illegal, and no one should be forced into marriage against their will. In practice, of course, people are going to be indoctrinated from a young age, misled, and pushed into marriage (polygamous or not), and we should find ways to stop that. Banning certain types of marriage is an ineffectual method, because polyamory is unenforceable.
It's a little different. Men and women are born at a 50/50 split. If married men in a town each marry 3 women, that means only 1/3 of the men can get married. This creates intense competition among males and is a contributor to the abuse against boys we often hear about as men in power try to drive out competition. It also lends itself to these child brides as there aren't any age appropriate women left. Not exactly the hallmarks of a healthy society. I go back and forth. I believe in religious freedom, but preventing a society like that seems important too.