The case, though framed as clash between free speech and gay rights, was the latest in a series of decisions in favor of religious people and groups, notably conservative Christians.

The decision also appeared to suggest that the rights of L.G.B.T.Q. people, including to same-sex marriage, are on more vulnerable legal footing, particularly when they are at odds with claims of religious freedom. At the same time, the ruling limited the ability of the governments to enforce anti-discrimination laws.

The designer, Lorie Smith, said her Christian faith requires her to turn away customers seeking wedding-related services to celebrate same-sex unions. She added that she intends to post a message saying the company’s policy is a product of her religious convictions.

A Colorado law forbids discrimination against gay people by businesses open to the public as well as statements announcing such discrimination. Ms. Smith, who has not begun the wedding business or posted the proposed statement for fear of running afoul of the law, sued to challenge it, saying it violated her rights to free speech and the free exercise of religion.

But when the Supreme Court agreed to hear the case, 303 Creative L.L.C. v. Elenis, No. 21-476, it agreed to decide only one question: “whether applying a public-accommodation law to compel an artist to speak or stay silent violates the free speech clause of the First Amendment.”

Both sides have said that the consequences of the court’s ruling could be enormous, though for different reasons. Ms. Smith’s supporters said a decision for the state would allow the government to force all sorts of artists to state things at odds with their beliefs.

Her opponents said a ruling in her favor would blow a hole through anti-discrimination laws and allow businesses engaged in expression to refuse service to, for example, Black people or Muslims based on odious but sincerely held convictions.

A divided three-judge panel of the U.S. Court of Appeals for the 10th Circuit, in Denver, applied the most demanding form of judicial scrutiny to the law but upheld it.

“Colorado has a compelling interest in protecting both the dignity interests of members of marginalized groups and their material interests in accessing the commercial marketplace,” Judge Mary Beck Briscoe wrote for the majority, adding that the law is narrowly tailored to address that interest.

“To be sure,” Judge Briscoe wrote, “L.G.B.T. consumers may be able to obtain wedding-website design services from other businesses; yet, L.G.B.T. consumers will never be able to obtain wedding-related services of the same quality and nature as those that appellants offer.”

Judge Briscoe added that “Colorado may prohibit speech that promotes unlawful activity, including unlawful discrimination.”

In dissent, Chief Judge Timothy M. Tymkovich, citing the writer George Orwell, said “the majority takes the remarkable — and novel — stance that the government may force Ms. Smith to produce messages that violate her conscience.”

“It seems we have moved from ‘live and let live,’” he wrote, “to ‘you can’t say that.’”

The Supreme Court considered a similar dispute in 2018 after a Colorado baker refused a create a custom wedding cake for a same-sex marriage. But that case, Masterpiece Cakeshop v. Colorado Civil Rights Commission, failed to to yield a definitive ruling.

Justice Anthony M. Kennedy, who wrote the majority opinion in the 7-to-2 decision in 2018, seemed unable to choose between two of his core commitments. He was the author of every major Supreme Court decision protecting gay rights under the Constitution. But he was also the court’s most ardent defender of free speech.

Instead of choosing between those values, Justice Kennedy chose an off ramp that not everyone found convincing. He wrote that the baker, Jack Phillips, should win because he had been treated unfairly by members of a civil rights commission who had made comments hostile to religion.

The court’s membership has changed since then, with the retirement of Justice Kennedy and the death of Justice Ruth Bader Ginsburg. Their successors, Justices Brett M. Kavanaugh and Amy Coney Barrett, shifted the court to the right.

Lower courts have generally sided with gay and lesbian couples who were refused service by bakeries, florists and others, ruling that potential customers are entitled to equal treatment, at least in parts of the country with laws forbidding discrimination based on sexual orientation.

The owners of businesses challenging those laws have argued that the government should not force them to choose between the requirements of their faiths and their livelihoods. Their opponents say that businesses open to the public must provide equal treatment to potential customers.