Parrish Clodfelter, a 79-year-old retiree who lives on a central North Carolina farm, professes opinions about transgender people that might get him fired if he worked for a multinational corporation, though for many here, they constitute simple country wisdom.

“A man wants to change to a woman, he’s got a mental problem,” Mr. Clodfelter said on Wednesday over lunch at Spiro’s Family Restaurant, where posters by the door advertised classes on carrying concealed weapons and a “Hillbilly Sunday” Pentecostal church service.

But Mr. Clodfelter has a different kind of problem. As a longtime Republican, he wants to support Pat McCrory, North Carolina’s Republican governor, in his re-election bid. At the same time, Mr. Clodfelter is worried about the boycotts and lost jobs resulting from the law the governor signed in March that limits transgender bathroom access and eliminates antidiscrimination protections for gay and transgender people.

If the backlash continues, Mr. Clodfelter said, he will consider voting for Mr. McCrory’s Democratic opponent, Roy Cooper, who supports the law’s repeal.

“I’m afraid if they don’t change it,” he said, “it’ll hurt the state.”

Even before the law tapped into a national debate about transgender rights, privacy and political correctness, North Carolina, the rare Southern state that is evenly split between liberals and conservatives, was considered to be up for grabs in the November presidential race, particularly if Donald J. Trump tops the Republican ticket.

Now the law, and the backlash against it, have introduced a different kind of volatile energy to state politics here, roiling a governor’s race that could be the nation’s most competitive. It is also affecting other crucial contests, including that of Senator Richard Burr, who hopes to fend off a vigorous Democratic challenge from Deborah K. Ross, a former State House member and former state director of the American Civil Liberties Union.

Last week, Mr. Burr, who has defended the law, came under attack from Democrats who have leapt at the chance to transform a cultural issue into an economic one, as the state has suffered the retreat of protesting companies, including PayPal, which canceled a plan to bring more than 400 jobs to Charlotte. On Thursday, the N.B.A. commissioner, Adam Silver, said the league would move its 2017 All-Star Game from Charlotte if the law were not changed.