She’s running with all she’s got for a seat she can’t win. That’s the point.

Kate Barr is waging a sure-to-lose campaign for a seat in the North Carolina legislature as a protest against gerrymandering, which has made elections uncompetitive in states nationwide. The result is a magnification of the state’s partisan advantage. The effect has been on particularly vivid display in some red states in recent years as legislators who have little to fear from a general election pass laws that are to the right of what their voters might support, experts say. Reproductive rights restrictions, school book bans and voting limitations have gone...