Ten days after raids by federal immigration officials in Los Angeles set off a national protest movement, a Hispanic woman walks through the city’s Canoga Park neighborhood. She says she won’t give her name for concern that she might risk trouble for herself or others. In fact, she won’t say much. But the quiet streets evoke a broader phenomenon sweeping the United States. “Right now, we’re hiding,” she says, noting that she’s a legal resident in a community where many others do not have...