Want That Job Offer? A Covid-19 Vaccine Is Now Required.

These mandates are in their early stages, making it tough to determine how many U.S. employers now require vaccines. Companies largely have been reluctant to require shots, at first because vaccines were scarce, and more recently because bosses feared blowback from their employees, employment attorneys and human-resources executives say.

The latest federal data show that half of American adults have had at least one shot, and vaccines are now open to all adults in the U.S. That’s made some employers feel more comfortable putting requirements in place. Polling suggests a swath of the population remains wary, hesitant because of the vaccines’ possible side effects, safety concerns or a mistrust of drugmakers or the government.

The Houston Methodist Hospital network is mandating vaccines for both existing employees and new hires, barring an exemption. Those who fail to comply will at first be suspended without pay, and later terminated, a hospital spokeswoman says. Houston Methodist believes employee vaccinations are essential to keeping patients safe.

“We saw this as a must-do,” Dr. Marc L. Boom, the hospital network’s chief executive, says of his organization’s decision to require vaccination. The system employs more than 26,000 people, from nurses and staff who interact with patients in clinical settings to administrative personnel who work outside of the hospital.

Companies can legally require vaccines as a condition of employment, though they must accommodate religious beliefs or medical conditions that may keep workers from getting shots, says Kevin Troutman, a partner at Fisher Phillips LLP who leads the firm’s vaccine work group. Employers can request proof of vaccination, though bosses run legal risks if they probe the reasons behind a worker’s hesitancy.

“The enforcement process can be pretty complicated,” Mr. Troutman says, adding that most companies requiring the shots give employees advance notice and months to comply. “I’m beginning to see a slow movement of more employers looking to require it.”

The mandates span industries and roles. In Alaska, a job listing for telecom company GCI Communication Corp. noted that a vaccine would be required to do work as a camp guide this summer, leading hikers and kayakers at a company retreat center. A spokeswoman for GCI declined to comment. In the San Francisco Bay Area, an ad for a human-resources assistant at the Boys & Girls Clubs of the Peninsula says in bold lettering that the applicant “MUST provide proof of COVID vaccination” or contact the organization’s HR team if eligible for an exemption.

The mandate for new staff mirrors the requirement the Boys & Girls Clubs of the Peninsula is putting in place for existing employees, says Chief Executive Peter Fortenbaugh. The shots will protect staff, as well as the children and families the organization serves, many of whom come from low-income communities hard-hit by the virus, he adds.

At meatpacking giant JBS USA Holdings Inc., a range of job openings at the company’s Colorado headquarters, including those for a fixed-asset accountant, environmental manager and corporate communications specialist state that it is a “job expectation” that new employees have at least one vaccine dose to start work.

JBS temporarily closed several plants following Covid-19 outbreaks last year and had 74 cases of Covid-19 at headquarters last October, according to state health records. A spokesman said the company has successfully held vaccination campaigns across its U.S. facilities and corporate offices, and is piloting the shot requirement for new hires at its corporate headquarters because of vaccines’ wide availability.

After Houston Methodist announced its mandate, Dr. Boom says he received hate mail from people outside of the organization, and some employees expressed frustration. Some staffers may choose to leave the organization instead of getting a shot, Dr. Boom says, though he predicts the vast majority will comply.

“We’re a scientifically based organization,” he says. “If somebody decides to leave because of that, honestly, they’re not a cultural fit.”

President Biden last week called on all companies—big and small—to offer paid time off for employees to get a Covid-19 vaccine dose or recover from any side effects, and he laid out details of a tax credit to help small businesses afford such leave.

Eleven Madison Park, a Michelin-starred restaurant and a trend-setter in the industry, lists several jobs requiring Covid-19 vaccination on its parent company’s careers page, including dining-room manager and maître d’. A spokeswoman declined to comment.

Legacy Restaurants in Houston, operator of local eateries the Original Ninfa’s and Antone’s Famous Po’ Boys, ran a two-day vaccine drive this month for all staff members and their spouses, partly to help them fulfill the company’s vaccine mandate for employees.

New hires are also asked to have at least one dose before they start, said Ana Fernandez, Legacy’s health and safety director. The vaccine drive has received little pushback she says. Most employees are grateful.

“We started asking everyone when the vaccine first came out, ‘Hey, how would you feel about getting it?’ And everyone was very willing,” says Ms. Fernandez.

At Lastique International Corp., a raw plastics distributor and recycler in Louisville, Ky. that employs roughly 50 people, the company’s owner wanted to require vaccines for all workers, including new hires. Kristen Manouchehri Oliveira, the company’s HR director, began researching how to implement it.

Lastique discussed the vaccine mandate in multiple meetings with workers in March and gave them until mid-April to receive their first dose. Ms. Oliveira coordinated with the local health department to help employees get shots.

Though most employees were on board, some balked, she says. One office worker quit, giving no notice. “We never saw her again,” Ms. Oliveira says.

Another employee resigned, saying he didn’t think the vaccine was for him. Ms. Oliveira says she’s held one-on-one discussions with staffers to explain the company’s position, but those conversations can be tricky. “I can’t really ask a lot of personal questions,” about why someone may be hesitant, she says.

The company now lists its vaccine requirements on its job ads for machine operators and others. She and her colleagues now open job interviews by asking: “Have you received the Covid vaccine, or are you planning to receive it?”

If an applicant is unwilling to do so, the interview ends. “It’s no problem at all,” she says. “It’s just you can’t work at Lastique.”

— Patrick Thomas contributed to this article.

Write to Chip Cutter at [email protected]