But a woman sitting nearby jumps in: “If Labor wants to change its image,” she says, “it’s Michal.”

At the very top, Israeli politics is consumed with the fate of Benjamin Netanyahu, the embattled prime minister, in April’s elections. But at the local level, the identity politics that divides Israelis in myriad ways — Arab and Jewish; Ashkenazi and Mizrachi; pro- and anti-settlement; secular and religious; left, right and center, and so on — has been producing unexpected results, nowhere more so than among the Jewish religious right.

In Beit Shemesh, a fast-growing ultra-Orthodox center, thousands ignored their rabbis’ orders and helped elect a woman mayor in October. In Bnei Brak, where Ms. Zernowitski was raised, Mr. Netanyahu’s Likud party won two seats, a signal achievement on a city council long dominated by Haredi parties. And in Telzstone, a tiny Haredi enclave on the outskirts of Jerusalem, an upstart who took on the rabbis’ anointed candidate in a special mayoral election last month earned 40 percent of the vote — a seismic shift, despite falling short, for a population that has long exerted power by voting in lock step.

The overwhelming majority of ultra-Orthodox still identify with right-wing policies, experts say. But those who do not are making their presence felt: In April’s elections, Adina Bar-Shalom, the daughter of the founder of one of the main Haredi parties, is running for Parliament on a social-justice platform and is widely expected to join a centrist ticket.

Ms. Zernowitski — who in keeping with modesty strictures wears a wig, but one so subtle it is impossible to notice — sees herself as embodying the generational yearnings of ultra-Orthodox voters who, unlike forebears who saw the land of Israel as holy but were uncertain about the state, want to feel more fully a part of the country in which they are citizens. “They’re trying to integrate into Israel and leave their ghettos,” she said.

As an advocate for women, too, she has an added motivation to break out of the confines of the Haredi world. After she finished a radio interview recently, she said, the station brought on a sitting Haredi lawmaker who said that women did not belong in politics just as they did not belong working at a garbage dump, “because politics is garbage.”