Walmart's new firearms policy has garnered strong reactions on both sides of the gun control debate.

But a poll from consumer research firm CivicScience indicates that the retail giant is going to be just fine, despite threats of a backlash.

A small majority of survey respondents said that the changes wouldn't affect their willingness to shop at Walmart.

A minority of survey participants said that the policy shift either adversely or positively affected their Walmart-related habits. Of that group, more people said that Walmart's new firearms policy left them "more likely" to shop at the national retail chain.

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Walmart's overhaul of its gun policy was met with praise from gun control advocates and criticism from their right-wing opponents.

Following a deadly mass shooting at its El Paso store that left 22 dead, the Arkansas-based company made the decision to bar the open carry of firearms in its stores, cut down on its ammo offerings, and ban the sale of handguns in Alaska.

The National Rifle Association in particular had harsh words for the retailer.

"It is shameful to see Walmart succumb to the pressure of the anti-gun elites," the NRA said in a statement on Twitter. "Lines at Walmart will soon be replaced by lines at other retailers who are more supportive of America's fundamental freedoms."

But, if recent history and a new poll are any indication, the firearms lobby's dire prediction may not pan out.

To get a sense of how customers are reacting to Walmart's open-carry policy change, consumer research company CivicScience polled 1,986 US-based Walmart shoppers based in the US.

The majority of survey participants — 52% in total — said that the new rules didn't impact their willingness to shop at Walmart.

When it came to the customers who said the decision would affect their Walmart-going habits, 29% of participants said they were "more likely" to make a shopping run at the national retailer. Of those respondents, 22% said they were "much more likely" to shop at Walmart.

Only 19% of respondents said they were less likely to frequent Walmart, including 14% who said they are "much less likely" to shop at the national retailer.

Read more: Walmart just overhauled its rules around gun sales in response to a series of deadly mass shootings — here's how supporters and critics reacted on Twitter

CivicScience also asked 1,471 Walmart customers about whether the retailer's decision to cut back on ammunition sales.

Once again, a small majority of respondents — 51% — said that the policy shift didn't affect their desire to shop at Walmart. A total of over 28% of respondents said that they were "more likely" to hit up the retailer, with 21% saying they'd be "much more likely" to spend money at the chain.

On the other hand, 20% of participants said the new ammo rules adversely affected their willingness to shop at Walmart, with 14% saying they were "much less likely" to patronize the stores.

Of course, Walmart isn't the only retailer to take a stand on firearms. But in the world of retail, companies are increasingly being cautious when it comes to firearms sales.

Kroger barred customers from openly carrying guns, just after the news about Walmart's policy update broke on Tuesday. Before that, Dick's Sporting Goods began gradually pulling guns from its shelves, while REI broke off its ties with gun brands. Dick's, Kroger, Walmart, and LL Bean also raised the minimum age from 18 to 21 for gun sales.

Those recent instances and CivicScience's latest study paint the picture of customers that largely don't plan to base their shopping habits off shifting firearms policies. And while Walmart's decision has clearly turned a minority of shoppers off, it's seemingly garnered the goodwill of a larger group of consumers.