GREER, S.C.—Global competition has turned South Carolina, the scene of a Republican primary on Saturday, into a trade powerhouse. Andrea Howell knows she is one of the winners but is wary nonetheless.

Mrs. Howell, a supervisor at BMW AG’s plant here, says working for the German company has given her job security, promotions and a fat enough salary to pay off two mortgages and put her daughter through college. “Working at BMW wasn’t just a job but a life-changer,” she says.

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