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“Just because you open a business doesn’t mean you set up a First Amendment-free zone,” Ms. Martin said. “There’s just no law or Supreme Court precedent that says when you engage in a commercial activity, you lose your free-speech rights.”

The ADF, which is considering filing an appeal, has a similar case in the pipeline. In August, the New Mexico Supreme Court ruled against Elane Photography, whose owners had refused to take photos at a same-sex commitment ceremony. Their attorneys have asked the U.S. Supreme Court to hear the case.

Neither Colorado nor New Mexico recognizes same-sex marriage. The Colorado men filing the complaint were married in Massachusetts, one of 16 states that, along with the District of Columbia, perform same-sex marriages.

Amanda C. Goad, staff attorney with the ACLU Lesbian Gay Bisexual and Transgender Project, said that while “religious freedom is important, no one’s religious beliefs make it acceptable to break the law by discriminating against prospective customers.”

“No one is asking Masterpiece’s owner to change his beliefs, but treating gay people differently because of who they are is discrimination plain and simple,” she said in a statement.