South Williamsburg, Brooklyn, just blocks from the hipster epicenter of Bedford Avenue, is home to one of the most conservative, separatist communities in the country: Satmar Hasidim, an ultra-orthodox arm of Judaism.

It’s a famously insular group. But lately, a rogue group within the Satmar community has been making noise. Calling themselves a “modesty committee,” its members, all men, keep tabs on the behavior of community members, teachers, and store owners to make sure that they adhere to principles of modesty. One result? Stores selling women’s clothes now rarely use mannequins in displays, which might arouse men and boys who pass by. Instead, clothes and wigs are modeled on faceless heads. Other, more disturbing allegations against these committees include ...