BERLIN—Emanuel Bernhard Krauskopf’s trips to his synagogue in the German capital have become an awkward affair.

The reason: Mr. Krauskopf and about 30 others recently founded a Jewish chapter of the Alternative for Germany, or AfD, an anti-immigrant party that is the largest opposition group in parliament—one whose members include people accused of anti-Semitism, right-wing extremists and others on the political fringe.

“I’m...