RALEIGH, N. C.—An outsider who was elected chairman of North Carolina’s Republican Party against the wishes of its leaders is in a feud with party brass—a fight that mirrors tensions in the national GOP and is hampering party activity in this swing state during an election year.

Chairman Hasan Harnett was barred from party headquarters in Raleigh last week and cut off from GOP email and other accounts after pushing to reduce the cost of a ticket to the party’s May 6-7 convention to zero from $90.

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