Mr. Jagsch’s party, known by its German initials N.P.D., has been on the political fringe since it was founded in 1964. The German government and both houses of Parliament have made various failed attempts to ban the party, most recently in 2017, when Germany’s highest court ruled that despite the party’s threat to the country’s Constitution and its Nazi links, it was not relevant enough to pose a real threat. The party won 0.4 percent of the vote in parliamentary elections that year.

“Now there is this great outrage,” an independent board member, Klaus Dietrich, told the Bild newspaper. “And I can understand that, but they should have had the courage to ban the party and then this problem would never have happened,” Mr. Dietrich said, referring to the establishment parties.

Ali Riza Agdas, a board member from the Social Democrats, told Bild that, in retrospect, it was a mistake to elect Mr. Jagsch, but that he was the only candidate.

Mr. Jagsch, 33, said the reaction to his appointment was “totally exaggerated and ridiculous,” and vowed to challenge the attempt to reverse the vote.

The effort reflected “a sad day for democracy,” he told the German news agency D.P.A.

On Thursday, he celebrated his appointment on his official Facebook page, which is marked with a banner decrying the “Lying Press” and where he has posted screeds against migrants, Muslims and established political parties, by saying “Of the people, for the people.”

Even outside of his neighborhood, where he is known to help collect the garbage and carry out other civic-minded duties, Mr. Jagsch is a well-known face of the N.P.D. He is deputy head of its state chapter in Hesse, has run for Parliament and in state elections, and has sought to become mayor of Altenstadt, the larger town of which Waldsiedlung is a district. Efforts to contact Mr. Jagsch via Facebook were unsuccessful.

State security officials also know him, because his name has surfaced in annual reports by the Hesse’s domestic security agency, which monitors individuals who are believed to pose a threat to the country and the Constitution.

“He’s not a nobody, he’s well connected within the Hessian scene,” said Jan Voss, a member of the Altenstadt city government and a Social Democrat. “So for me it’s just shocking that he was voted in.”