KERRVILLE, Texas—When Texas Gov. Greg Abbott said he would lift the statewide Covid-19 mask mandate, he left businesses in charge of setting and enforcing their own policies. H-E-B, a beloved Texas grocer and a stalwart during past crises in the state, waffled.

The company, which had experienced a string of altercations in its aisles over mask policy, initially said it would urge customers to wear masks, but require them of employees. A few days later, after some shoppers and workers criticized the grocer, the chain clarified its stance. It would leave up signs and keep making announcements stating that masks are required, and offer them to maskless shoppers. H-E-B also said it would continue its policy of not escalating situations in which a customer refuses to wear a mask.

The shift in H-E-B’s message reflects the balancing act that many businesses in Texas now face after the state put them in charge of setting and enforcing mask policy. Since the mandate was lifted on March 10, some H-E-B employees and customers say they have noticed more maskless customers shopping the aisles.

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After the chain’s initial statement that it would urge customers to wear masks, H-E-B President Scott McClelland told the Houston Chronicle that the governor’s move stripped stores of the “backstop” that the threat of a fine provided, which he said could lead to more people entering stores without masks. Mr. McClelland said he had to weigh the physical well-being of customers and employees, given the frequent disputes over masks in stores even when state mask rules were in effect.

“Of all the issues we have dealt with over the course of the last year, masks are the most polarizing,” Mr. McClelland told the Chronicle. “In part, because they were used as a political weapon and in part because, frankly, people don’t like wearing masks.”

H-E-B said it expects shoppers to continue wearing masks in its stores and that it has increased security at many of its locations. “The ending of mask ordinances puts real pressure on retailers to enforce an emotional policy for many and we will not ask our Partners to put themselves in harm’s way,” the company said in a written statement.

Gov. Greg Abbott, here in February, rescinded the mask mandate on March 10.

Photo: Bob Daemmrich/Zuma Press

Several H-E-B employees said they have noticed an uptick in the number of people not wearing masks since Mr. Abbott’s announcement. An employee at an H-E-B in the Bryan-College Station area of eastern Texas said that during the mandate he would notice an unmasked shopper perhaps every hour or so. Last week, as an experiment, he began taking a tally of people not wearing masks during one of his shifts. In about five hours, he saw 38 people without masks.

The employee said he wished H-E-B would take a stronger stance in favor of masks, though he said he understood it would be difficult to implement. “They don’t want chaos and fighting at their stores,” he said. “I don’t think it’s an easy choice, by any means…but it’s the right thing.”

At an H-E-B in Kerrville, a small town in central Texas’s Hill Country, employees didn’t appear to bother the few unmasked shoppers who showed up on Friday morning last week.

“I don’t like people telling me what to do,” said a male customer. “Let me make that decision.”

Some of the biggest retail, theater, hotel and restaurant chains said they planned to continue requiring masks in Texas, Mississippi and other states that lifted restrictions.

Many local business owners cheered the policy shift, particularly in hard-hit sectors such as restaurants that are desperate to bring back customers. In a March survey of more than 700 restaurants conducted by the Texas Restaurant Association, 44% of respondents said they would no longer require face coverings of their customers.

Anthony Fauci, the U.S. government’s top infectious-disease doctor, says it is risky to curb public-health measures, because coronavirus cases could plateau and then rebound.

H-E-B, founded by the Butt family in 1905, has more than 400 stores throughout the state. The chain was lauded for its pandemic preparation when Covid-19 first struck, has been a major competitor in the rollout of vaccines and is regularly praised for its response to hurricanes and other disasters.

Katy Bravenec, 37 years old, said she lost faith in H-E-B after its initial statement and no longer plans to shop at her San Antonio store. Ms. Bravenec said she scouted out three H-E-B’s after the mask mandate was lifted to see whether customers were allowed to shop maskless. After seeing a handful of customers not wearing masks at each store, she said she would take her business to a nearby Trader Joe’s.

“It didn’t fit with their public image,” she said. “You can’t claim to be a strong community partner and then lift the mask mandate when it’s not only there for your workers but for our community. It just seemed hypocritical.”

Wendy Wright shops at an H-E-B in Houston but said she would consider switching to the nearby Kroger Co. KR -1.51% store if she notices an increase in maskless shoppers. Ms. Wright said she has been to H-E-B twice since the Republican governor rescinded the mask mandate. On the first trip, she estimated that about 10% of shoppers were maskless. She gave the store one more chance this past Sunday and didn’t notice any customers or employees without a mask.

“I’ll take it week by week and if it seems like a safe place to shop I’ll stay. If they let masks slide, I’ll go to another store,” she said. “I’m 60, I don’t want to play with Covid.”

‘The more we talked about it, it didn’t seem right to enforce it because it’s not a law.’

— Augie Bering V, owner of Bering’s hardware stores in Houston

Other Texas businesses have wrestled with whether and how to respond to the lifting of restrictions.

In Pearland, the Good Vibes Burgers & Brews restaurant told local media when the mandate was lifted that it was scrapping all mask requirements. A day later, on March 11, the company said all employees would wear masks and that it would hand out disposable ones to any customer who wanted one. A company spokeswoman declined to comment.

Augie Bering V, owner of Bering’s hardware stores in Houston, said it was a relief when Texas put a mask mandate in place over the summer. Since then, he said, few unmasked people have visited the stores. Lifting the mask order put business owners in a difficult position, he said.

“We got put in the middle,” he said. “Some of the conversations we had were, ‘We need to require it so we can enforce it.’ But the more we talked about it, it didn’t seem right to enforce it because it’s not a law. People could see it as a political thing.”

Nearly everyone at the Kerrville H-E-B was masked on Friday morning last week, two days after the mandate was lifted. The choices are largely regional, said Rachel Townsend, 24, a mental-healthcare worker. She notices many more people wearing masks in Kerrville, which has a high retiree population, than in her hometown of Uvalde in southern Texas, she said.

In Fort Worth, Tatiana Miller, 39, said she sympathizes with Texas businesses caught in the mask debate. Ms. Miller said businesses have no way of enforcing a mask policy, with or without a mandate. She said she agreed with the policy of urging customers to wear a face covering, but not making it mandatory for entry.

“Texans like their choice. It would be easier for people to decide what they should do or not do,” she said. “I do feel like businesses can’t win.”

Write to Patrick Thomas at [email protected] and Elizabeth Findell at [email protected]

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