The bolded part seems like a new question. It is one thing to consider open relationships morally acceptable, and another whether it is moral to deny the right to polygamy.
In a society where we all bear the outcomes of bad decisions, we do things like pass laws about marriage, inheritance, child protection, and other private matters. If experience bears out that open relationships end up causing a strain on society, IOW cause more problems, result in more kids without stable homes, result in more divorce or legal issues and people dependent upon the state because of failed marital agreements, then it is moral to object to polygamy and open relationships.