One lay nun whose order has deep roots in Mindong said Bishop Zhan would have difficulty running the diocese because most worshipers are in the underground church and support Bishop Guo. Still, she said that if the Vatican recognized Bishop Zhan, she would obey.

Though weakened by migration and buffeted by change, Mindong remains a place where one can still sense the world of the Dominican friars who first brought Catholicism to these hilly shores in the 1630s — and the powers of faith that can outlast politics.

Not far from Bishop Guo’s cathedral is Shangwan Village, the burial site of a Catholic priest named Miu Zishan who was persecuted by Communist zealots in the 1960s and died shortly after.

In front of his grave, Wu Saiqing, 49, was sleeping on a stone bed. Locals believe that doing so cures illnesses, and so Ms. Wu was there for a midday nap, hoping to improve her health.

Ms. Wu said her family’s Catholic roots dated to the 17th century. Two of her siblings serve the official church, one as a nun and one as a priest. But she attends an underground church.

“It makes no difference to me,” Ms. Wu said. “It is the Lord we believe in.”