Donald Trump gets strong support where churches, civic groups and safety net are in trouble; discombobulated Reading, Pa.

This coal and steel region was thriving when Gary Martin started working construction sites in the mid-1970s. Ironworkers jammed the local union hall, the union sponsored a big picnic each spring, and business groups were flush with volunteers for charity drives. Mr. Martin’s extended family attended church, as it had for generations, in an area called Irish Valley in neighboring Schuylkill County. Two-parent families were the norm, and fatal drug overdoses were so rare that some county coroners didn’t bother tallying them. No longer. Working-class neighborhoods, in particular white ones hit hard by the decline of the U.S. industrial base, are crumbling under the weight of deepening social problems. Mr. Martin, 63 years old, retired last year as head of Ironworkers Local 420 but financially supports three grandsons—22, 21 and 19—because his daughter became an addict. The oldest grandson turned to heroin, too, and Mr. Martin and his wife got divorced in another casualty of the stress, they say. “Rather than spending my retirement half-time in Ireland as I planned, I moved back to the house with a dirt-floor basement where I grew up to try to help raise my grandchildren,” he says.

The buckling of social institutions fundamental to American civic life is deepening a sense of pessimism and disorientation, while adding fuel to this year’s rise of political populists like Donald Trump and Bernie Sanders. Here and across the U.S., key measures of civic engagement ranging from church attendance to civic-group membership to bowling-league participation to union activity are slipping. Unlocked doors have given way to anxiety about strangers. In Reading, tension between longtime white residents and Hispanic newcomers has added to the unease.

Across the U.S., the Republican presidential nominee has his firmest support among the white working class.

In Berks County, once famous for the Reading Railroad stop on the Monopoly board game, social ills have been exacerbated by a 30% decline in manufacturing jobs and 6% fall in inflation-adjusted median income since 1995. In 2014, 55.2% of the white women in Berks County who gave birth hadn’t finished college and were unmarried, up from 16.5% in 1980, according to Bowling Green State University’s National Center for Family and Marriage Research. Single mothers had a median income of just $22,378 in 2014, less than half that of the typical household in Berks County and the U.S. overall.

Some economists say the decline of institutions that fortify communities has a negative impact on household income. Without the strong support system from those networks, known as social capital, some people miss work more often during times of need, and their children have fewer extracurricular activities and other ways to get ahead.

Social problems in white working-class communities nationwide started to escalate in the 1970s. The number of single parents in those places rose, and so did divorces and the number of men who dropped out of the workforce, says Charles Murray, a political scientist at the conservative American Enterprise Institute, who has worked to quantify the decline of working-class America.

Those problems seemed to ease briefly in the late 1990s as the economy expanded and the crime rate dropped. President Bill Clinton and lawmakers revamped the U.S. welfare system in 1996 to focus more on jobs. The nationwide divorce rate stabilized, as did the percentage of children born to unwed mothers. Regular church attendance held steady.

Many Hispanics have lived in the Reading area for decades, moving here for jobs as agricultural workers, and say they belong in the community as much as anyone else. Some community groups try to bridge the gap between whites and Hispanics, but the results sometimes fall flat. Reading’s Downtown Improvement District co-sponsors free outdoor concerts during the summer, but a concert in August attracted a nearly white-only audience.

“We pick up trash and make things look pretty,” Mr. Snyder says. “You don’t need a college degree for this; you don’t need a lot of skills. But you’re getting together with people you don’t know to bring about a common purpose.”

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