“It all flipped, so fast,” said Mr. Odgaard, a patrician 70-year-old who favors khakis and boat shoes. “Suddenly, we were in the minority. That was kind of a scary feeling. It makes you wonder where the Christians went.”

The beginning of the end of the Odgaards’ familiar life came Aug. 3, 2013, when Lee Stafford and Jared Ellars arrived at the Odgaards’ gallery, Görtz Haus. The couple were in a panic because the hotel they had booked for their wedding had gone bankrupt two months before the date, and they had already sent the invitations out. Mr. Odgaard spent about 45 minutes showing them the property and figuring out seating, flowers and how many guests needed gluten-free meals. It was only when Mr. Odgaard asked if it was a same-sex wedding that his tone changed, they said.

“I’ll remember these words for the rest of my life,” said Mr. Ellars, 35, a database administrator. “He looked at us and he said, ‘I can’t take your money, and we don’t do anything for free.’”

The couple, together for 13 years, say they never wanted the Odgaards to go out of business. They say they wanted them to stop discriminating against gay people and never put another gay couple through the rejection they experienced. The case was settled in arbitration, and the Odgaards had to pay $5,000 to Mr. Stafford and Mr. Ellars, which they donated to an anti-bullying program for gay students.

Their wedding was held in a barn, officiated by a minister with the Disciples of Christ church that Mr. Stafford attends. To this day, Mr. Stafford, who is 43 and a business systems analyst, is troubled that the debate over religious liberty appears to be “so one-sided,” he said.

“Their religious beliefs say they don’t approve of gay marriage, but my religious beliefs say that we can,” he said. “Why does their religion trump mine?”