Can You "Identify" As a Women During Women-only hours at public swimming pool in Brooklyn ?

The Atlantic reports:

This week, a public pool in Brooklyn became the diving-off point for a new clash over religious law and religious coercion in New York City. For decades, the Metropolitan Recreation Center in Williamsburg has offered gender-separated swimming hours in an accommodation to the heavily Hasidic Jewish community that it serves.

After an anonymous complaint was lodged about its summer schedule, which includes two primetime hours of women-only swimming on Sunday afternoons, the city rescinded and then reaffirmed the right of the pool to maintain its separate hours. Some, a little less anonymously this time, registered dismay over the decision.

“Four times a week this summer —Mondays, Wednesdays and Fridays from 9:15 to 11 a.m., and Sunday afternoons from 2:45 to 4:45—a public swimming pool on Bedford Avenue in Brooklyn will be temporarily unmoored from the laws of New York City and the Constitution, and commonly held principles of fairness and equal access,” a local-edition New York Times editorial began. Explaining that Jewish law forbids women to bathe in front of men, the paper, echoed by a not insignificant chorus on social media, inveighed against what it called “a theocratic view of government services.”

Why can't men "identify" as women and show up in progressive Brooklyn?