“I’m actually thinking more that I am going to go Libertarian,” Ms. White, 42, said after wrestling with a mannequin at the apparel store she and her husband recently opened.

For decades, this state has embodied contradictory impulses, simultaneously electing a racial hard-liner like Jesse Helms and New South Democrats like Terry Sanford and Jim Hunt. But, as its demographics shift, discerning which way the state will tilt in November seems harder than ever.

North Carolina may be the most evenly divided presidential battleground in the country.

Its two biggest population centers, Charlotte and the so-called Research Triangle of Raleigh, Durham and Chapel Hill, have been transformed by an influx of political centrists from other states. The fastest-growing party registration preference is not Republican nor Democrat, but unaffiliated. The rural white “Jessecrats,” conservative Democrats who reliably cast ballots for Mr. Helms, are dying off. Elections are now won in the fast-growing edge towns like Cary, outside Raleigh, which natives joke stands for Containment Area for Relocated Yankees.

Neither Mr. Trump, with his hard-edge nationalism, nor Mrs. Clinton, with a swirl of scandal surrounding her, is a natural fit for a state that hungers for political moderation but is increasingly disenchanted with the political class.

“They don’t like either party and they don’t like either candidate,” said Carter Wrenn, a veteran Republican strategist here. “It will just depend on which one they dislike less on Election Day.”

Polls show Mr. Trump and Mrs. Clinton begin the general election close to evenly matched. The surest sign of a jump ball: Democrats believe Mr. Trump starts with a narrow advantage, while Republicans believe Mrs. Clinton does. What they agree on is that, as at the national level, Republicans are largely coalescing around Mr. Trump and ruling out the possibility that Mrs. Clinton could run away with the state.

Then again, Mr. Trump needs North Carolina much more than Mrs. Clinton does.

With his difficulties among Hispanic voters pushing typical swing states such as Colorado, Nevada and Florida toward the Democrats, Mr. Trump will probably need to carry the combined 28 electoral votes from North Carolina and Virginia to capture the White House.