Justice Samuel A. Alito Jr. on Tuesday renewed his criticisms of the Supreme Court’s landmark decision recognizing the right to same-sex marriage, saying that people who oppose homosexuality risk being unfairly “labeled as bigots and treated as such.”

The justice included his warning in a five-page statement explaining why the court had rejected a request to hear a Missouri case about people removed from a jury after voicing religious objections to gay relationships. The case, Justice Alito added, “exemplifies the danger” from the court’s 2015 decision, Obergefell v. Hodges.

The ruling, he added, shows how “Americans who do not hide their adherence to traditional religious beliefs about homosexual conduct will be ‘labeled as bigots and treated as such’ by the government.”

The statement appeared to offer a glimpse into Justice Alito’s continued discontent with Obergefell v. Hodges, in which the court, by a 5-to-4 vote, guaranteed a right to same-sex marriage, a long-sought victory in the gay rights movement.

In the years since, Justice Alito and Justice Clarence Thomas, who both dissented from the 2015 decision, […]