RALEIGH, N.C. — On a Wednesday in late October, canvassers wearing hot-pink T-shirts with messages like “abortion rights voter” and “abortion is on the ballot” fanned out across neighborhoods in Wake County and knocked on door after door.

Each had grabbed a stack of door hangers with the message “Vote for your reproductive freedom champions” above the names of candidates.

Technically, abortion is not on the ballot here. North Carolina is one of more than a dozen states that have…