Today, the agency has classified about a third of all AfD members as extremist, including Mr. Chrupalla and Alice Weidel, the party’s other lead candidate. A court is reviewing whether the entire party can soon be placed under formal observation.

“The AfD is irrelevant in power-political terms,” said Mr. Funke. “But it is dangerous.”

Mr. Chrupalla, a decorator who occasionally takes the stage in his overalls, and Ms. Weidel, a suit-wearing former Goldman Sachs analyst and gay mother of two, have sought to counter that impression. As if to hammer home the point, the party’s main election slogan this year is: “Germany — but normal.”

A look through the party’s 207-page election program shows what “normal” means: The AfD demands Germany’s exit from the European Union. It calls for the abolition of any mandates to fight the coronavirus. It wants to return to the traditional German definition of citizenship based on blood ancestry. And it is the only party in Parliament that denies man-made climate change, while also calling for investment in coal and a departure from the Paris climate accord.

That the AfD’s polling numbers have barely budged for the past 18 months suggests that its supporters are not protest voters but Germans who subscribe to its ideas and ideology.

“The AfD has brought out into the open a small but very radical electorate that many thought we don’t have in this country,” said Mr. Quent, the sociologist. “Four years ago people were asking: ‘Where does this come from?’ In reality it was always there. It just needed a trigger.”

Mr. Quent and other experts estimate the nationwide ceiling of support for the party at around 14 percent. But in parts of the former Communist East, where the AfD has become a broad-based political force entrenched at the local level, it is often twice that — enough to make it the region’s second-strongest political force.

Among the under 60-year olds, Mr. Quent said, it has become No. 1.

“It’s only a question of time until AfD is the strongest party in the East,” Mr. Quent said.

That is why Mr. Chrupalla, whose constituency is in the eastern state of Saxony, the one state where the AfD already came first in 2017, predicts it will eventually become too big to bypass.

“In the East we are a people’s party, we are well-established at the local, city, regional and state level,” Mr. Chrupalla said. “In the East the middle class votes for the AfD. In the West, they vote for the Greens.”

Christopher F. Schuetze and Melissa Eddy contributed reporting.

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