PORTLAND, ORE.—An appellate court Thursday upheld a penalty against Oregon bakery owners who refused to make a cake for a same-sex wedding almost five years ago.

The owners of the since-closed Gresham bakery — Aaron and Melissa Klein — argued that state Labor Commissioner Brad Avakian violated state and federal laws by forcing them to pay emotional-distress damages of $135,000 to the lesbian couple.

Their lawyers said Avakian and the state Bureau of Labor and Industries violated the Kleins’ rights as artists to free speech, their rights to religious freedom and their rights as defendants to a due process.

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But the Oregon Court of Appeals sided with the state Thursday, saying the Kleins failed to show the state targeted them for their religious beliefs. The judges also found public statements made by Avakian before deciding the case did not establish a lack of impartiality.

“Today’s ruling sends a strong signal that Oregon remains open to all,” Avakian said in a statement after the 62-page opinion was released Thursday. Adam Gustafson, the attorney who argued the Kleins’ appeal, did not immediately return a phone message.

The decision comes weeks after the U.S. Supreme Court heard arguments in the high-profile case of a Colorado baker who refused to make a wedding cake for a same-sex couple.

That baker, Jack Phillips, claims his First Amendment claims of artistic freedom were being violated — a similar issue raised by the Kleins.

The Oregon court said the Kleins’ argument that their cakes entail an artistic expression is “entitled to be taken seriously,” but it’s not enough for the couple to assert their cakes are pieces of art — they must show others perceive their creations like a sculpture or painting.

“Although we accept that the Kleins imbue each wedding cake with their own esthetic choices, they have made no showing that other people will necessarily experience any wedding cake that the Kleins create predominantly as ‘expression’ rather than as food,” the opinion says.

The state penalized the bakers after determining they violated a 2007 Oregon law that protects the rights of gays, lesbians, bisexual and transgender people in employment, housing and public accommodations. The law provides an exemption for religious organizations but does not allow private businesses to discriminate based on sexual orientation.

The case began when Rachel Bowman-Cryer went to the suburban Portland bakery with her mother in January 2013. They met with Aaron Klein, who asked for the date of the ceremony and the names of the bride and groom.

When told there was no groom, Klein said he was sorry but the bakery did not make cakes for same-sex weddings. According to documents from the case, Rachel and her mother left the shop, but returned a short time later. As Rachel remained in the car, in tears, her mother went in to speak with Klein.

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The mother told Klein she had once thought like him, but her “truth had changed” when she had two gay children. Klein responded by quoting Leviticus: “You shall not lie with a male as one lies with a female; it is an abomination.”

Rachel and Laurel Bowman-Cryer praised the ruling in a statement released through their attorney: “It does not matter how you were born or who you love. All of us are equal under the law and should be treated equally. Oregon will not allow a ‘Straight Couples Only’ sign to be hung in bakeries or other stores.”