Also Monday, on the second anniversary of the court's decision finding a constitutional right for gay couples to marry, the justices overturned an Arkansas court's ruling that allowed different treatment on birth certificates for married heterosexual couples and same-sex ones.
The plaintiffs were two lesbian couples who conceived children through artificial insemination.
The case of the Denver baker is similar to lawsuits brought elsewhere involving florists, calligraphers and others who say their religious beliefs won't allow them to provide services for same-sex weddings. But these objectors have found little success in the courts, which have ruled that public businesses must comply with state anti-
The decision to grant the case came as a surprise, because the court first considered it last September. It was continually relisted for further discussion at the private conferences at which the justices decide which cases to take.
That indicates that Phillips's request that the court take the case was bolstered by the addition of Justice Neil M. Gorsuch, who has displayed a deeply conservative streak since joining the court in April. The case will be heard in the term that begins next October.
In 2014, the justices declined to revisit a New Mexico Supreme Court decision that found that a photographer violated a state civil rights law when she declined to photograph a lesbian couple's commitment ceremony.
In the Colorado case, David Mullins and Charlie Craig visited Masterpiece Cakeshop in July 2012, along with Craig's mother, to order a cake for their upcoming wedding reception. Mullins and Craig planned to marry in Massachusetts, where same-sex marriages were legal at the time, and then hold a reception in Colorado.
But Phillips refused to discuss the issue, saying his religious beliefs would not allow him to have anything to do with same-sex marriage. He said other bakeries would accommodate them.
The couple filed a complaint, and in 2014, the Colorado Civil Rights Commission determined that Phillips's action violated state law. That ruling was upheld in Colorado state courts.
Phillips's lawyers stressed artistic freedom more than the baker's religious beliefs in their reaction to Monday's Supreme Court announcement.
"Every American should be free to choose which art they will create and which art they won't create without fear of being unjustly punished by the government," said David Cortman, senior counsel for Alliance Defending Freedom. "It imperils everyone's freedom by crushing dissent instead of tolerating a diversity of views. We are all at risk when government is able to punish citizens like Jack just because it doesn't like how he exercises his artistic freedom."
The American Civil Liberties Union represents Mullins and Craig. "The law is squarely on David and Charlie's side because when businesses are open to the public, they're supposed to be open to everyone," said James Esseks, director of the ACLU's LGBT Project.
Craig said in a statement: "While we're disappointed that the courts continue debating the simple question of whether LGBT people deserve to be treated like everyone else, we hope that our case helps ensure that no one has to experience being turned away simply because of who they are."
The Supreme Court ruled in 2015's Obergefell v. Hodges that marriage is a fundamental right that states may not prohibit to gay couples. But how that decision affects related issues has generated numerous legal battles.
The justices settled one of those battles with their ruling in the Arkansas case, Pavan v. Smith, reversing the state Supreme Court and saying the state must list same-sex parents on birth certificates.
When a woman gives birth in Arkansas, state law generally requires that the name of the woman's male spouse appear on the birth certificate, regardless of his biological relationship to the child. But the state court said that rule did not have to be followed if the mother was married to a woman.
To refuse to list both women on the birth certificate, the court's unsigned opinion said, is to deny married couples "access to the 'constellation of benefits that the state has linked to marriage,' " quoting the Obergefell decision.
Elsewhere around the country, the Washington Supreme Court found that Barronelle Stutzman, owner of Arlene's Flowers in Richland, Wash., violated a state civil rights law that bars discrimination in public businesses on the basis of sexual orientation. The court also ruled that the law does not infringe on her free speech.
The Texas Supreme Court is considering a challenge to Houston's provision that gives the same benefits to spouses of gay workers as it does to those of straight workers. Gay rights activists say the Obergefell decision should have settled the issue.