WASHINGTON — The Supreme Court said Monday that it would hear a major religious liberties case that could grant new freedoms to businesses to discriminate against gays and lesbians — and potentially others — based on the faith of the owners.

The case involves the Christian owner of a Colorado bakery who refused to make a wedding cake for a same-sex couple.

The high-profile dispute pits the rights of religious individuals against gay rights, two issues that have been at the forefront of several recent Supreme Court decisions. Both are high priorities for Justice Anthony M. Kennedy, whose vote in this matter will probably be key.

In the past, Kennedy has been both a strong supporter of gay rights and a defender of religious liberty.

The Colorado case is likely to become one of the court’s most contentious cases next term. It could decide whether business owners are allowed to cite their religious views as a reason for refusing to serve gay and lesbian couples. Potentially, it could sweep even more broadly, opening a religious exemption to civil rights laws that could allow discrimination against other groups.

The case, to be heard in the fall, could have a wide effect in states like California that prohibit discrimination against people based on their sexual orientation.

No federal law requires businesses to serve all customers without regard to their sexual orientation, but 21 states have “public accommodations” laws that prohibit discrimination against gays and lesbians.

States with such anti-discrimination laws are mostly in the West, East Coast and upper Midwest. No state in the South or on the Great Plains has such a law.

Colorado is one of the states whose laws protect gay couples, and Jack Phillips, the owner of the Masterpiece Cakeshop in Lakewood, Colo., was charged with violating it.

In 2012, he said he politely declined to make a wedding cake for Charles Craig and David Mullins, who had planned to marry in Massachusetts but then have a reception in their home state of Colorado. They lodged a complaint with the state civil rights commission.

The commission ruled that Phillips’ refusal to make the wedding cake violated the provision in the state’s anti-discrimination law that says businesses open to the public may not deny service to customers based on their race, religion, gender or sexual orientation. The panel ordered him to provide wedding cakes on an equal basis for same-sex couples.

Phillips appealed to the Supreme Court, arguing he deserved a religious exemption based on the 1st Amendment’s guarantee of freedom of speech and free exercise of religion. His lawyers say he refused to comply with the commission ruling while his appeal proceeded.

They described Phillips as a “cake artist” who will “not create cakes celebrating any marriage that is contrary to his understanding of biblical teaching.”

They also said he has refused to make cakes to celebrate Halloween or create baked goods that have “anti-American or anti-family themes” or carry profane messages.

“They said you have to create cakes for same-sex couples, so he removed himself from the market. He chose to stop making wedding cakes,” said Jeremy Tedesco, a lawyer for the Alliance Defending Freedom, who appealed on Phillips’ behalf.

Lawyers for the state commission and the American Civil Liberties Union urged the court to turn down the appeal in Masterpiece Cakeshop vs. Colorado Civil Rights Commission. They said it could open a “gaping hole” in civil rights laws if business owners could cite their religious beliefs as a valid basis for denying service to certain customers.

“This has always been about more than a cake,” Mullins said in a statement. “Businesses should not be allowed to violate the law and discriminate against us because of who we are and who we love.”

James Esseks, director of the ACLU’s LGBT Project said 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.”

But Justice Kennedy, who wrote the court’s opinion upholding same-sex marriages, has also joined the court’s conservatives in upholding religious exemptions. He joined the 5-4 majority in the Hobby Lobby case, which said the Christian family who owned a chain of craft stores could refuse to provide their employees the full range of contraceptives called for by the federal healthcare law.

Public opinion polls show that most Americans support the rights of same-sex couples to marry and that support has steadily increased, even among groups who have been opposed in the past, notably evangelical Christians.

Advocates on the Christian right, however, say the government should not force believers to endorse marriages that conflict with their faith.

Two years ago, the justices turned down a similar appeal from a wedding photographer in New Mexico. Since then, the issue has arisen in several other states whose laws forbid discrimination based on sexual orientation.

The appeal in the Colorado case has been pending since January, suggesting the justices were closely split on what to do. Justice Neil M. Gorsuch, a Colorado native and a well-known defender of religious liberty claims, joined the court in April.

It takes only four votes to hear the case, and on the last day before the summer recess, the justices announced they would hear the issue during the fall.

Separately Monday, the court in a 6-3 ruling struck down an Arkansas law regarding birth certificates that prevented adding the names of both parents in a same-sex union. The law called for including only the biological parent.

The court, in an unsigned opinion, said this rule denied the same-sex couple the same rights as opposite-sex couples and was therefore unconstitutional.

The court noted that in Arkansas if an opposite-sex couple used artificial insemination with an anonymous sperm donor to have a child, the mother’s husband in such a case would be listed on the birth certificate.

Justices Clarence Thomas, Samuel A. Alito Jr. and Gorsuch dissented in that case, Pavan vs. Smith.

david.savage@latimes.com

Twitter: DavidGSavage