The justices left in place a unanimous state Supreme Court ruling last year that said Elane Photography violated New Mexico's Human Rights Act by refusing to photograph the same-sex ceremony "in the same way as if it had refused to photograph a wedding between people of different races."
Elane Photography co-owner Elaine Huguenin said taking the photos for Vanessa Willock and her partner would violate her religious beliefs. She said she also has a right of artistic expression under the First Amendment that allows her to choose what pictures to take, or refrain from taking. She was ordered to pay more than $7,000 in attorneys' fees, which Willock waived.
The case has been cited as lawmakers in other states have proposed legislation exempting people from such lawsuits if doing business with same-sex couples violates their religious beliefs.
Arizona passed such a law this year, but Republican Gov. Jan Brewer vetoed it under pressure and blistering criticism from major corporations and political leaders from both parties.
Similar religious-protection legislation has also been introduced around the country. And eight states, Alabama, Arizona, Kansas, Michigan, Montana, Oklahoma, South Carolina and Virginia, had asked the high court to hear the case so lawmakers would have guidance in considering such measures.
Russell Moore, president of the Ethics & Religious Liberty Commission of the Southern Baptist Convention, said "at issue is the fundamental question of whether the state can pretend to be a god over the conscience."
The American Civil Liberties Union countered that regardless of personal beliefs, "every business has to play by the same rules to protect customers from discrimination in the marketplace."
An Arizona-based group, Alliance Defending Freedom, represented the Albuquerque studio.
"Only unjust laws separate what people say from what they believe," said Alliance Defending Freedom Senior Counsel Jordan Lorence. "The First Amendment protects our freedom to speak or not speak on any issue without fear of punishment. We had hoped the U.S. Supreme Court would use this case to affirm this basic constitutional principle; however, the court will likely have several more opportunities to do just that in other cases of ours that are working their way through the court system."
The group said it is also defending cases like those of a Washington state florist and a Colorado cake artist who refused to do work for same-sex couples and a Kentucky T-shirt printer who declined to make shirts promoting a gay pride festival.
Tobias Barrington Wolff, a University of Pennsylvania law professor representing the couple, said "no court in the United States has ever found that a business selling commercial services to the general public has a First Amendment right to turn away customers on a discriminatory basis.
"The New Mexico Supreme Court applied settled law when it rejected the company's argument in this case, and the Supreme Court of the United States was correct to deny certiorari review. The time had come for this case to be over, and we are very happy with the result."
AP National Writer David Crary in New York and newsman Mark Sherman in Washington contributed to this report.