A federal judge has struck down parts of Utah’s anti-polygamy law as unconstitutional in a case brought by a polygamous star of a reality television series. Months after the Supreme Court bolstered rights of same-sex couples, the Utah case could open a new frontier in the nation’s recognition of once-prohibited relationships.

Judge Clark Waddoups of United States District Court in Utah ruled late Friday that part of the state’s law prohibiting “cohabitation” — the language used in the law to restrict polygamous relationships — violates the First Amendment guarantee of free exercise of religion, as well as constitutional due process. He left standing the state’s ability to prohibit multiple marriages “in the literal sense” of having two or more valid marriage licenses.

Judge Waddoups, who was appointed by President George W. Bush, wrote a 91-page decision that reflects — and reflects upon — the nation’s changing attitude toward government regulation of personal affairs and unpopular groups. The Supreme Court supported the power of states to restrict polygamy in an 1879 decision, Reynolds v. United States.

Judge Waddoups made clear that the Brown case was not an easy one for him, writing, “The proper outcome of this issue has weighed heavily on the court for many months.” He noted the shifts in the way the Constitution has been interpreted over the past century to increase protection for groups and individuals spurned by the majority.

“To state the obvious,” Judge Waddoups wrote, “the intervening years have witnessed a significant strengthening of numerous provisions of the Bill of Rights.” They include, he wrote, enhancements of the right to privacy and a shift in the Supreme Court’s posture “that is less inclined to allow majoritarian coercion of unpopular or disliked minority groups,” especially when “religious prejudice,” racism or “some other constitutionally suspect motivation can be discovered behind such legislation.”

The challenge to the law was brought by Kody Brown, who, along with his four wives and 17 children, stars in “Sister Wives,” the reality television show. The family argued that the state’s prohibition on cohabitation violated its rights to privacy and religious freedom. The Browns are members of the Apostolic United Brethren Church, a fundamentalist offshoot of the Mormon Church, which gave up polygamy around 1890 as Utah was seeking statehood.

The judge cited the decision in Lawrence v. Texas, the 2003 Supreme Court case that struck down laws prohibiting sodomy. He quoted the majority opinion by Justice Anthony M. Kennedy that stated the Constitution protects people from “unwarranted government intrusions into a dwelling or other private places” and “an autonomy of self that includes freedom of thought, belief, expression and certain intimate conduct.”

In a statement, Mr. Brown said he and his family were “humbled and grateful for this historical ruling from the court today.” He noted that “many people do not approve of plural families,” but “we hope that in time all of our neighbors and fellow citizens will come to respect our own choices as part of this wonderful country of different faiths and beliefs.”

As same-sex marriage has gained popular approval and legal status in recent years, some have hoped — and some feared — that other forms of cohabitation might follow. Justice Antonin Scalia, in his bitter and famous dissent from the 2003 Lawrence case, said the nation was on the verge of the end of legislation based on morality, and was opening the door to legalizing “bigamy, same-sex marriage, adult incest, prostitution, masturbation, adultery, fornication, bestiality and obscenity.”

Jonathan Turley, a law professor at George Washington University who represented the Browns in this case, disagreed with Justice Scalia’s reasoning and said in an exchange of emails that the case “is about privacy rather than polygamy.” He added, “Homosexuals and polygamists do have a common interest: the right to be left alone as consenting adults. There is no spectrum of private consensual relations — there is just a right of privacy that protects all people so long as they do not harm others.”

Utah’s attorney general’s office has suggested in the past that it would appeal any decision that struck down the polygamy law. Attorney General John Swallow resigned last month under a cloud of multiple investigations, and his replacement has not been named.

Mr. Turley said an appeal by the state would be unwise, adding, “Utah has been on the wrong side of history in fighting privacy, and they would now be on the wrong side of the law as well.”