LINCOLN, Neb. — When Nebraska lawmakers defied Gov. Pete Ricketts in 2015 by repealing the death penalty over his strong objections, the governor wouldn’t let the matter go. Mr. Ricketts, a Republican who is Roman Catholic, tapped his family fortune to help bankroll a referendum to reinstate capital punishment, a measure the state’s Catholic leadership vehemently opposed.

After a contentious and emotional battle across this deep-red state, voters restored the death penalty the following year. Later this month, Nebraska is scheduled to execute Carey Dean Moore, who was convicted of murder, in what would be the state’s first execution in 21 years.

The prospect has renewed a tense debate in a state that has wrestled with the moral and financial implications of the death penalty for years, even before the 2015 attempt to abolish it. Protesters have been holding daily vigils outside the governor’s mansion to oppose Mr. Moore’s execution.

Complicating matters, Pope Francis this week declared that executions are unacceptable in all cases, a shift from earlier church doctrine that had accepted the death penalty if it was “the only practicable way” to defend lives. Coming only days before the scheduled Aug. 14 execution here, the pope’s stance seemed to create an awkward position for Mr. Ricketts, who is favored to win a bid for re-election this fall.