BOISE, Idaho—Far-right agitator Ammon Bundy’s emerging bid to become the next governor of Idaho faces a peculiar roadblock: he is currently barred from entering the state Capitol where he would ostensibly need to conduct official business after being arrested there twice within 24 hours. But his campaign, teased in the filing of paperwork last month if not yet official, is anything but a joke. These days, Bundy—who along with his father Cliven...