Mr. Dominguez worries about bringing the virus home and infecting his wife and two children. He would prefer to stay off the job until the worst of the coronavirus pandemic passes, but he needs the money to feed his family.

“It’s about necessity,” the 33-year-old said.

The construction industry is at the heart of the debate over how to safeguard public health while also preventing the economy from grinding to a halt. Builders contend with a patchwork of state and local rules for working during the pandemic, and governments are constantly re-evaluating their restrictions.

Frontline workers like Mr. Dominguez are trying to make sense of rules in one municipality allowing only emergency work, while a few miles away construction on a luxury apartment building can proceed under broader state regulations.

Unions in Massachusetts have clashed with the state over its policy allowing the continuation of a range of construction activities, including housing developments. They would like to see the state shut down almost all building sites, as Boston quickly did on March 17.

Jimmy Williams, vice president of the International Union of Painters and Allied Trades, said coronavirus presents “the biggest Catch-22 we’ve ever been faced with,” go to work amid a life-threatening pandemic or lose one’s job.

“There’s definitely a growing sentiment in the industry that we are being put at risk,” he said.

Construction is one of the largest sectors of the economy, with about 7.6 million workers, according to the U.S. Bureau of Labor Statistics. Many federal and state officials have said it is important to keep the business of building on course as the U.S. faces a potentially deep and lengthy recession.

North America’s Building Trades Unions, along with the Associated General Contractors of America and the U.S. Chamber of Commerce, successfully lobbied the federal government in late March to include construction on its list of essential industries. Many states have at some point followed that guidance, allowing varying ranges of construction work to continue amid the health crisis.

Restrictions differ state to state and within states. Pennsylvania and Vermont have shut down virtually all projects. In California, Gov. Gavin Newsom greenlighted construction at the state level, but health directors in seven counties, including San Francisco, issued stay-at-home orders in mid-March that halted almost all local construction.

“In a perfect world we’d have one standard” across the country, said Sean McGarvey, president of NABTU.

Organized labor accounts for about 40% of nonresidential construction work in the U.S., according to NABTU. Some unions, both at the national and local level, have urged state and local leaders to further halt construction. Those decisions have been tough calls for union leaders because if their members aren’t on the sites working they aren’t getting a paycheck.

Boston was one of the cities that moved quickly to shut down construction activity, apart from emergency work, essential maintenance and building hospitals and shelters to meet pressing needs.

Mayor Martin Walsh, a former construction worker himself, said he knew that it would be difficult for most sites to provide a safe environment to prevent the spread of the virus.

“For some of these larger sites there was no way of policing them the way they needed to be policed at that moment,” Mr. Walsh said.

His administration will soon impose new requirements for essential construction. Builders will have to file a signed affidavit certifying safety compliance and detailed Covid-19 countermeasures such as providing workers with protective equipment and wash stations with running water, as well as strategies to maintain social distancing on a site. Those requirements, which are being introduced Monday, will extend to all construction sites when they are allowed to reopen.

The 75,000-member Massachusetts Building Trades Council voted unanimously on March 31 to call on Gov. Charlie Baker to declare a statewide suspension of regular construction projects at least through the end of this month.

The state hasn’t changed its guidance, though it updated guidelines with more specific construction-safety protocols. That prompted two major unions in Massachusetts to direct their members to stay home for at least the month of April.

One of the unions was the North Atlantic States Regional Council of Carpenters, and initially its Massachusetts members were split, with some saying that earning money and benefit hours was a priority. Later, however, “it became clear that conditions on construction sites in Massachusetts were abnormally dangerous, even in circumstances where contractors and members were making their best efforts,” said Bert Durand, a spokesman for the regional carpenters’ union.

Over the weekend, the union revoked its stay-at-home order for work deemed essential in Massachusetts after reaching an agreement with contractors. Builders are now required to submit for review pandemic safety plans for sites where members work. If plans are lacking or aren’t followed, the union would direct its members to cease work at that location.

At the construction site for a luxury apartment building in Lynn, Mass., union members videotaped workers getting out of a packed car and working closely side by side with no masks or other gear to guard against infection. One worker said he resorted to using a ski mask and porous gloves after being told to get his own protective equipment. The developer eventually shut down the construction site.

The inconsistency of rules is roiling the labor pool, said local developer Robert Korff. With Boston jobs shut down, he initially saw a doubling of job seekers at his residential project in nearby, less-restrictive Newton, making social distancing even more challenging. He said he had to send many of them home.

Despite safety assurances, workers remain concerned. “In general, construction companies tend to look really good on paper,” Mr. Dominguez, who is from El Salvador, said in Spanish through an interpreter. “But there aren’t enough checks to see if safety is there.”