The U.S. Supreme Court on Tuesday heard 90 minutes of arguments in a case that pits religious conviction against discrimination based on sexual orientation.

In 2012, Jack Phillips, the owner of Denver-based Masterpiece Cakeshop, refused to consider baking a cake for Dave Mullins and Charlie Craig. The men married in Massachusetts and wanted to buy a cake from Phillips for their Denver reception. Phillips said that serving the couple would violate his religious faith. Colorado at the time recognized gay and lesbian couples with civil unions, not marriage.

The couple sued, saying that Phillips' faith does not give him a right to discriminate, and a Colorado court found that Phillips had discriminated against the men under Colorado law. After the Colorado Supreme Court declined to hear an appeal, Phillips turned to the Supreme Court, arguing that the First Amendment protects his religious rights.

(Related: Baker who refused gay couple says Jesus would do the same.)

Justice Anthony Kennedy, considered the swing vote, sent mixed messages about how he's leaning in the case. Kennedy questioned how Colorado officials handled the case, accusing the Colorado Civil Rights Commission of being “neither tolerant, nor respectful of Phillips' religious beliefs.” He also mentioned “other good bakery shops that were available.”

Jack Phillips is represented by the Alliance Defending Freedom (ADF), an Arizona-based Christian group opposed to LGBT rights.

U.S. Solicitor General Neil Francisco, representing the Trump administration, also argued on behalf of Phillips. He told the justices that denying a wedding cake to a same-sex couple was based not on identity, as would be the case with an interracial or black couple, but on the act of same-sex marriage.

Kennedy asked Francisco whether a ruling in Phillips' favor would allow owners to post signs stating that they do not serve gay people. He answered that that was true in some cases.

“I think that he could say he does not make custom-made wedding cakes for gay weddings, but most cakes would not cross that threshold,” Francisco said.

The case, Masterpiece Cakeshop vs. Colorado Civil Rights Commission, is the high court's first related to LGBT rights since it decided Obergefell, the 2015 landmark ruling that found that gay and lesbian couples have a constitutional right to marry. A ruling is expected in June.