The Supreme Court ’s conservative majority sounded sympathetic Monday to a Christian graphic artist who objects to designing wedding websites for gay couples, a dispute that’s the latest clash of religion and gay rights to land at the highest court.

The designer and her supporters say that ruling against her would force artists — from painters and photographers to writers and musicians — to do work that is against their faith. Her opponents, meanwhile, say that if she wins, a range of businesses will be able to discriminate, refusing to serve Black customers, Jewish or Muslim people, interracial or interfaith couples or immigrants, among others.

The lively arguments at the Supreme Court ran well beyond the allotted 70 minutes.

Justice Neil Gorsuch, one of three high court appointees of former President Donald Trump, described Lorie Smith, the website designer, as “an individual who says she will sell and does sell to everyone, all manner of websites, (but) that she won’t sell a website that requires her to express a view about marriage that she finds offensive.”

The issue of where to draw the line dominated the questions early in Monday’s arguments at the high court.

Justice Ketanji Brown Jackson asked whether a photography store in a shopping mall could refuse to take pictures of Black people on Santa’s lap.

“Their policy is that only white children can be photographed with Santa in this way, because that’s how they view the scenes with Santa that they’re trying to depict,” Jackson said.

Justice Sonia Sotomayor repeatedly pressed Kristen Waggoner, the lawyer for Smith, over other categories. “How about people who don’t believe in interracial marriage? Or about people who don’t believe that disabled people should get married? Where’s the line?” Sotomayor asked.