(CNN) — When Cowbell, a comfort food restaurant in New Orleans, started requiring proof of vaccination for indoor dining, some customers were less than thrilled.

Cowbell put the rule in place starting July 29, advertising the requirement with a sign on its door and a post to its website. A few weeks later, on August 16, New Orleans began requiring indoor diners to show proof of vaccination or a recent negative Covid-19 test.

“We got a few F-Bombs the first day,” said Brack May, who co-owns the restaurant with his wife Krista Pendergraft-May. Some people were angry even though they were vaccinated.

“They just were like, pissed off they had to show [their cards],” he said.

Twice, May recalled, there was a rift when couples were asked to show proof of vaccination. “The wife was showing the card and the husband’s like, ‘I’m not F-ing doing this,’ and walked out,” he said.

The restaurant also got some messages criticizing its rule. One message viewed by CNN Business states conspiracy theories, calling Covid fake and the Earth flat. May tried to explain his thinking behind the vaccine requirement by reaching out to some of the critics. “I called as many people [who complained] as I could to say that for me, it’s an issue of courtesy,” May explained. “It’s no different than opening a door for somebody. That’s the way I feel about it.”

In a handful of US cities, including New York and San Francisco, people who eat indoors at restaurants have to show proof that they are vaccinated. Increasingly, restaurants that are not in these cities are making their own rules, like requiring vaccines or negative Covid-19 tests, in an effort to keep staff and customers safe.

Requiring proof of vaccination may seem like a clean solution: Customers are vaccinated and allowed in — or not, and asked to dine outside or take items to go.

But it’s far from easy. Restaurants have gotten backlash from customers and critics in far-flung locations. Some aren’t sure how to implement the rule, or to walk the line between serving guests and policing their behavior.

“The challenge for operators right now is complying with rapidly evolving rules, without a lot of guidance, without a lot of support,” said Sean Kennedy, executive vice president of public affairs at the National Restaurant Association.

Nasty criticism and angry customers

Hark! Cafe in Minneapolis began requiring proof of vaccination on Tuesday. Customers are also asked to wear masks inside regardless of vaccination status, according to Katherine Pardue, chef and co-owner of the plant-based restaurant.

When they come up to order at the counter — there’s no table service — a staffer asks if they want to eat indoors, she said. If they say yes, they have to present proof of vaccination or a negative Covid-19 test from the past 48 hours. Minneapolis doesn’t have any such rule in place for restaurants.

While customers have not been upset by the policy and business has actually gone up, the restaurant has gotten criticism via “phone calls, email, social media messages [and] social media posts,” Pardue said, often from people outside of the city. One Facebook comment viewed by CNN Business likens what Hark is doing to segregation.

“It’s really unfortunate that the rhetoric around vaccines is so politicized, when we do not view it as a political issue,” she said. “It is our right as business owners to do this,” she added. “Customers can make the decisions that are best for them. Anyone can choose to eat here or not eat here. And we can choose to make these rules.”

Not everyone has seen their sales rise. New York City requires people who eat indoors to show proof of vaccination as of August 16, with enforcement slated to begin September 13. Once it starts enforcing the rule, the city plans to fine businesses that are not in compliance.

Art Depole, who co-owns the burger joint Mooyah in Times Square along with his brother, says he opposes the current mandate primarily because of the impact on his business.

At Depole’s restaurant, sales were down about 25% last week compared to the previous one. Depole noted that about a fifth of his staffers have said they might quit because they don’t want to be vaccinated or don’t want to disclose their vaccination status, as required by the city’s mandate.

The Mooyah restaurant is located at the bottom of a hotel and currently has no outdoor dining space. Its clientele is made mostly of office workers — a dwindling demographic, as offices extend their remote policies — and tourists, who are confused or angered by the new rule, Depole said.

“People from out of town … literally do not have anything that they can show us,” he said, because they don’t have the city or state’s vaccine app downloaded to their phones, and don’t have physical cards with them. Some question the restaurant’s right to ask medical questions. “‘I’ve had groups of seven or eight come in … if six are vaccinated and two aren’t, then I have to turn away [the] whole group,” he said.

It’s never easy to turn people away. Still, restaurant owners like Josh Weinstein say they’ve felt relief since instituting a vaccination policy.

Weinstein, owner of The Quiet Few in Boston, said that when he announced that his bar, which also serves food, would require proof of vaccination for indoor dining it “took pounds upon pounds off my shoulders.” Boston does not require restaurant customers to be vaccinated, so Weinstein made the call on his own. As a type 1 diabetic with a young child, Weinstein is personally relieved to know that customers who dine in his restaurant are vaccinated. He’s gotten backlash to the decision through email, phone and social media, but feedback from his regulars has generally been “fantastic,” he said.

But he noted in an Instagram post announcing the rule that it was a difficult decision to make. “It sucks. It’s tough. We hate it. But it needs to be done,” he added. “We hope you understand our position in this. And if you don’t agree, we hope we can mend our ways down the road.”

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