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NEW YORK — Drug chains CVS and Walgreens as well as grocery chain Wegmans Food Market have joined the chorus of retailers requesting that customers refrain from openly carrying firearms in their stores even where state laws allow it.

The announcements on Thursday follow similar moves by Walmart, the nation’s largest retailer, as well as Kroger earlier this week. Walmart also said it would stop selling handgun and short-barrel rifle ammunition in the aftermath of a string of mass shootings, including one last month inside an El Paso, Texas store that killed 22 customers — the deadliest in the company’s history.

Starbucks, Wendy’s and Target have already asked customers not to openly carry guns in stores unless they’re law enforcement officers. But the retailers have stopped short of introducing an outright ban because they say they don’t want to put employees in confrontational situations. Ken Perkins, president of research firm RetailMetrics, says retailers can’t have their workers, who get paid $15 an hour, trying to pry a gun away from an armed shopper.

Walmart and other big national chains cater to all kinds of customers with different views on guns but store policies have recently been trending toward more restrictions.

“There’s nothing more important than the safety of our customers and employees,” said Wegmans in a Twitter post. “The sight of someone with a gun can be alarming, and we don’t want anyone to feel that way at Wegmans. For this reason, we prefer that customers not openly carry firearms in our stores.”

Retailers are increasingly feeling the need to protect their workers while also keeping customers safe. At the same time, Perkins believes that any restrictions, including on open carry policies, may discourage gun enthusiasts from patronizing their stores.

Still, it’s a risk some retailers are willing to take.

“The tide is changing in terms of what people are willing to put up with,” Perkins said. “People’s patience is wearing thin.”