Polygamy after Windsor: What’s Religion Got to Do with It? Although First Amendment jurisprudence would subject polygamy bans to a higher level of scrutiny, this heightened protection comes at a cost. The landmark same-sex marriage case, United States v. Windsor, and the opinion’s protected liberty interest of “equal dignity” provide polygamy advocates with substantive grounds to protect their plural marriage practices, as well as pave the way for recognition of “intimate pluralism” and alternative relationship forms like polyamory and group marriage.