Mr. Moster said his goal was to advocate systemic change, not to punish specific institutions. He also sent a concerned letter to the State Board of Regents, which oversees the State Education Department. He received a response that said that “although there is an equivalency of instruction requirement,” nonpublic schools “largely operate outside the scope of state-mandated general education requirements and oversight.”

Image The billboard that Mr. Moster’s advocacy group, Yaffed, sponsored in Brooklyn last year reads, in Hebrew: “You must provide your son a proper education.” Credit... Courtesy of Naftuli Moster

To Mr. Moster, this meant that the state was acknowledging its responsibility and then willfully ignoring it.

He went to Albany to plead his case in person but said the meetings were unproductive.

The state department would not discuss Mr. Moster’s letter to the Board of Regents with The New York Times or speak about the equivalency mandate except to say that enforcement was the city’s responsibility. For its part, the city said the state was responsible.

So now Mr. Moster is taking legal action. A handful of modern Orthodox supporters have agreed to cover the legal fees and, with Mr. Moster, are interviewing lawyers. The plaintiffs in a lawsuit, however, must be either students who are currently enrolled in Hasidic schools or their parents. Mr. Moster said many families in New York’s Hasidic enclaves were sympathetic to his cause. So far, a small number of parents have agreed to take part in a lawsuit if they can remain anonymous. They worry that the yeshivas will expel their children and that the community will ostracize them if their names are revealed.

Mr. Moster is also a potential liability to his own project. Secular education pushed him away from his Hasidic roots. The formal break came after Mr. Moster filed for a “dependency override” from his family — proof that he was no longer a dependent — in order to apply for financial aid. In doing so, Mr. Moster went “off the derech,” or “off the path.” He said that he felt free but that his community considered him a disgrace.

Today, instead of black trousers, a white shirt and a broad, black hat, Mr. Moster wears V-neck sweaters and plaid button-down shirts. He still considers himself “very Jewish,” but that’s not how many ultra-Orthodox Jews see him. Once, he said, on the subway, a Hasidic mother instructed her son to “stop looking at the goy” — the non-Jew. She was talking about Mr. Moster.

Last year, Yaffed sponsored a billboard near the Prospect Expressway in Brooklyn with a quotation in Hebrew from the Talmud, “You must provide your son a proper education.” Below that was a caveat in English. “It’s your mitzvah” — or religious commandment — it said. “It’s the law.”