The CDC’s new mask policy — allowing vaccinated people to largely ditch their masks — is putting retailers in a tough spot.

Labor unions are now demanding large retail chains go against the CDC’s advice and continue to insist all customers wear masks to protect employees.

But retailers say they don’t want to act as the mask police, a practice that resulted in violent altercations even when the CDC recommended masks in all public settings.

“We are not a police force and can’t ask customers for proof of vaccinations,” said Avi Kaner, owner of Big Apple supermarket chain Morton Williams.

Ditto for employees, Kaner said.

In fact, the Morton Williams chief recently asked the union that represents his employees, Local 338, whether the chain could require its employees to be vaccinated in order to work in its stores. “The union said absolutely not,” he said.

“As soon as the governor lifts the mandate, we will leave it up to the discretion or our employees and customers, giving them the freedom to do what they want to do,” Kaner said.

Adding to the confusion, the federal government’s guidance does not supersede state and local laws. New York Gov. Andrew Cuomo has not yet lifted the state’s mask mandate as he reviews the CDC’s new guidelines.

A hodgepodge of approaches are being rolled out in the wake of the CDC’s new guidelines, which say fully vaccinated people can forgo masks indoors and outdoors except in certain circumstances, such as crowded indoor settings.

Macy’s, Target, CVS and Kroger are all reviewing the new guidance, while Walmart, the nation’s largest retailer, said it will no longer require vaccinated workers and shoppers to wear masks in municipalities that allow it.

Trader’s Joe’s has also reportedly said on its website that fully vaccinated customers will no longer be required to wear masks.

The supermarket’s “COVID 19 update” lifting the mask mandate no longer appears to be available, however. Trader Joe’s didn’t immediately return a request for comment.

Labor unions, meanwhile, have made it clear that they are not happy about the development.

“People who work in public facing jobs — such as in supermarkets and other retail establishments — will still need to be protected,” Stuart Appelbaum, president of the Retail, Wholesale and Department Store Union, said in a statement. “They have no way of knowing whether customers who are not wearing masks have been vaccinated. These workers, many of whom are essential, may be exposed both to the virus and to unnecessary stress. We must encourage customers in high trafficked areas to continue wearing masks.”

Applebaum also blasted the CDC for requiring masks in crowded places, a concept that can be left open to interpretation. “We don’t know what constitutes a congested area. A supermarket or a concert?,” he said.

“We need more information from the CDC about why … it’s safe for someone in a supermarket to be exposed to people carrying the virus and it’s not safe on trains and airplanes.”

The sentiment was echoed by the United Food and Commercial Workers International union head, Marc Perrone, who said Thursday, “Today’s CDC guidance is confusing and fails to consider how it will impact essential workers who face frequent exposure to individuals who are not vaccinated and refuse to wear masks.”

The restaurant industry is also struggling with how to respond to the new federal guidelines.

“Because restaurants welcome people who are both vaccinated and not fully vaccinated, operators will still need to work with their state and local regulators to ensure they are in line with all other mandates,” the National Restaurant Association’s senior vice president, Larry Lynch, said in a statement. “For this reason, the association won’t be immediately updating its COVID-19 operating guidance.”