JPMORGAN asked many of its roughly 37,000 employees in the New York metro area this week to work from home in staggered shifts to stem the spread of the COVID-19 virus. Bank tellers, who account for about half its New York workforce, weren’t included.

Fiat Chrysler Automobiles NV sent 14,000 mostly white-collar workers from its US headquarters to work from home Thursday. Factory workers were required to show up at their plants, including one in Kokomo, Indiana, where a worker had tested positive for the virus.

About 70% of America’s workers don’t have the luxury of working from home, including people like bank tellers, factory workers and those who labor in such industries as waste hauling, retail and health care. These 100 million people are likely to be the last ones at work even as the rest of their colleagues set up shop in home offices or at kitchen tables.

The split is raising thorny legal and fairness issues for corporations, from, Inc. to Procter & Gamble Co., that understandably want to isolate workers while the highly communicable disease continues to spread. It’s “making very, very visible a lot of the kinds of inequalities that have long been in place,” said Erin Hatton, an associate professor of sociology at the University of Buffalo who studies race, gender, class and inequality.

“What this public-health crisis is doing is making those dynamics and those inequalities kind of part of the problem of this public health crisis,” Ms. Hatton said.

The issue is playing out across corporate suites, in many permutations. Companies are being forced to make hard choices about how quickly they should implement continuity plans, how to communicate them without causing panic and how to keep morale up for workers who can’t telecommute.

Amazon sent much of its office staff home, but left in place workers who operate warehouses, and the contractors who deliver packages vital to people stuck at home.

Procter & Gamble sent office staff home Thursday but also operates more than two dozen factories making vital products such as toilet paper and disinfectants. The Gap sent white-collar workers home in New York and San Francisco as thousands of retail locations remain open.

Even in Italy, where cases have surged, grocery stores, pharmacies and some banks are still open, meaning people have to come to work even as the global death toll tops 5,000, including 1,000 in Italy. The US toll stands at 36.

Companies face a risk of claims from employees getting different treatment, but generally the law allows such disparities, said Derek Barella, a labor and employment lawyer at the Schiff Hardin LLP law firm in Chicago.

“You need to make sure that we have a legitimate reason for why we’re treating some people differently than others, and it has to be based on the job,” Mr. Barella said. “It is true, and it will be true, that a lot of jobs are capable of being performed remotely, whereas others are not.”

The United Auto Workers has raised the issue with Fiat Chrysler and other companies, seeking paid leave for workers who self-quarantine. While union contracts cover sick leave, there’s uncertainty regarding workers who have to isolate themselves to prevent the spread of the virus. General Motors Co. and Ford Motor Co. have also asked white-collar employees to work from home.

“The UAW feels strongly that no member should be disadvantaged in response to the COVID-19 process,” Cindy Estrada, a union vice-president, wrote in an e-mail to members.

The issue came to a head at Fiat Chrysler’s Windsor, Canada, minivan plant, where employees have refused to go to work since Thursday after a factory worker self-quarantined, a company spokeswoman said. The Canadian Ministry of Health has determined the plant is safe and the automaker is meeting with the union to try to get workers to return, the spokeswoman said.

Even with a clear concept and good intentions, plans can go awry in the rapidly changing environment, as JPMorgan discovered.

JPMorgan had moved faster than most other US banks in implementing measures, such as restricting non-essential travel for its entire work force and asking staff to test remote access capability.

On Monday, it was prepared to go further by implementing a staggered work-from-home policy for roughly a third of its 127,137 consumer-unit employees who work from corporate offices across the country. But it put the plan on pause while leaders debated what would happen if implemented company-wide and how to communicate what could be a touchy issue given the branch employees and call-center operators, people familiar with the talks said earlier this week.

It wasn’t until New York state sought business help that the bank implemented on Thursday a staggered work-from-home plan for its New York-area employees.

Wells Fargo & Co., which also has thousands of branches, has been testing limited work-from-home capabilities this week. Morgan Stanley, Goldman Sachs Group, Inc., BlackRock, Inc. and Citigroup, Inc. asked portions of their staff to work from home in rotating shifts.

Retail giant Costco Wholesale Corp., which is based in Issaquah, Washington, bucked the trend altogether, so far, telling headquarters workers to stay at their desks unless ill.

“We know some home office employees would like to work remotely, but our jobs here are to support our retail business, and we’re not prepared at this point to have corporate employees work from home,” the company told employees. “This decision may be unpopular with some, but we consider it a matter of equity and fairness.”

The growing awareness of the gap between workers has prompted some corporate adjustments for employees who can only work at work.

Walmart, Inc. announced a new emergency-leave policy for its hourly workers after a store employee tested positive for the coronavirus. The retailer will allow employees to stay home if they are unable to work or feel “uncomfortable” at work, according to a memo seen by Bloomberg. To be paid for the time, employees will still need to use regular paid time-off options, it said.

“What this is bringing to the fore is just how important these front-line service workers are to our service economy,” said Erin Hatton, the University of Buffalo professor. “And in my ideal vision, businesses would come out of this, as well as the government, with a better sense of ‘Wait, we need to take care of these workers because our economy is only as robust as these workers are protected.’” — Bloomberg