The latest Utah polygamy case [SL Trib link] is by a trio not yet entered into polygamy, who argue that "the state of Utah should not be able to criminalize the maintenance of an intimate relationship." Well, there's prostitution, statutory rape, and incestuous unions, all of which are acceptably criminalized or "regulated" intimate relationships, so it's hard to affirm the general rule. The plaintiffs also argue that "the [state's] ban on plural marriage violates their constitutional rights to practice their religion and to free association." Reynolds redux, that won't fly.
But when they argue that "the law unfairly targets religious polygamy because people who create multiple common-law marriages through cohabitation are never prosecuted for bigamy," this highlights the potential to frame the state's prohibition on polygamy as contravening the Lukumi Babalu Aye principle that religious practices cannot be targeted while identical or similar secular practices are ignored. The state argued that polygamy laws are enforced across the board, regardless of the religious motivations or affiliations of the participants, and that the state has a right to define marriage legally and enforce marriage laws. This case might show how far Lawrence v. Texas can be made to stretch. The Deseret News story on the suit provides additional details (a better discussion, actually).