ERFURT, July 4 -- From the motorway bridges outside the city, demonstrators hung from harnesses and abseiled to block the access roads. Behind them, more than 200 buses arrived from across Germany, carrying roughly 20,000 people who had come to surround the conference centre where the far-right Alternative for Germany party was holding its annual congress.

The protesters did not stop the conference. The AfD's congress opened on schedule.

What played out in Erfurt on Saturday was not simply a demonstration against a political party. It was a confrontation with a party that has become Germany's second-largest force in parliament, one that now polls high enough to take control of an eastern state government for the first time since 1932, a...