“We’re going to have litigation in Alabama, I am certain of it,” Mr. Albritton said, “over whether probate judges have a choice to accept or decline to issue the license and conduct the ceremony.”

In Kentucky, the A.C.L.U. suit is the nation’s first legal test, post-Obergefell, of how far a public official can go in resisting the decision. Ms. Davis is one of two county clerks — the state has 120 — who have defied Governor Beshear’s directive. She is also suing the governor, claiming that he violated her religious freedom.

“Her case will go nowhere,” said Katherine Franke, an expert on sexuality law, as well as religious exemptions, at Columbia Law School, earlier this week, adding that previous cases in which public officials have sought not to perform their duties on religious grounds have ended much the same way. “She doesn’t get to pick and choose which of her duties she will perform.”

But Christian conservatives are watching closely.

“This case could be a marker of how the religious freedom aspects of same-sex marriage are going to be worked out,” said Roger Gannam, who represents Ms. Davis on behalf of Liberty Counsel, a nonprofit organization in Florida that specializes in religious exceptions cases. “Many in Christian circles believe we are only now beginning the culture wars over marriage.”

Those culture wars are playing out with vigor in Morehead and Rowan County, where some churches sent congregants by the busload to rally for Ms. Davis when she appeared in court. “We feel very proud of her,” said the Rev. Harley Sexton Jr. of Sharkey Freewill Baptist Church, “that she has taken a religious stand against the state.”

Image April Miller and Karen Roberts displayed their gemstone bands. Credit... Jessica Ebelhar for The New York Times

But Morehead is also home to Morehead State University, which gives the city a liberal streak. At a downtown coffee shop and bookstore, where organic soaps and locally made jewelry share display space with books, even patrons uncomfortable with same-sex marriage said this week that Ms. Davis must follow the new law of the land.