By Martha C. White

Chick-fil-A is playing a high-stakes game of chicken that has nothing to do with its sandwiches.

President Dan Cathy’s public stance on gay marriage kicked off a firestorm that could hurt its sales and growth prospects, although restaurant analysts say support from the religious right in core markets could make the overall business impact a wash. But to sustain this uneasy equilibrium, the company has to avoid saying or doing anything to further inflame two opposing groups of consumers.

The Atlanta-based food chain is fending off accusations of hostility to the LGBT community following Cathy’s comments in support of traditional marriage and the “biblical definition” of families.

Then came the backlash to the backlash: A second elected official in Chicago challenged the push to keep the company from opening a new restaurant there, Republican politicians Mike Huckabee and Rick Santorum voiced their support for the company, and supporters rallied around the idea of a “Chick-fil-A Appreciation Day.”

On Friday, New York City’s Mayor Michael Bloomberg weighed in, saying that it’s “none of the government’s business.”

A few days after Cathy’s statements became public, Chick-fil-A issued a statement saying, “Going forward, our intent is to leave the policy debate over same-sex marriage to the government and political arena.”

That would be wise, said Tim Calkins, professor of marketing at the Kellogg School of Management at Northwestern University.

The emergence of two strong, polarized public responses puts the company in a tough spot, he said. “There are people who strongly support their position, which means the company can’t backpedal too much,” he said. “They could risk turning off a significant number of customers” with expressions of solidarity for either camp.”

“I’m not sure they should be trying to make one customer group happy over another,” said Eric Giandelone, director of food service research at Mintel. “From a food perspective, [they should] try and bring in as many customers as they can.”

Analysts are divided on to what extent this controversy will affect the company’s bottom line. “I don’t think it’s going to make much of a difference in the long term,” Giandelone said. “They’re almost kind of netting each other out.”

This effect isn’t going to be homogenous, though; when the dust has settled, there could be a much sharper delineation between which markets are friendly to Chick-fil-A and which aren’t. This appears to be happening already: According to a YouGov BrandIndex survey, the chain’s reputation among consumers fell sharply in nearly all regions of the country following Cathy’s remarks. The exception was the Midwest, where its score climbed higher for a brief period of time, then returned to its previous position.

In markets like the Bible Belt, where the company has its roots, “It will probably strengthen their brand and strengthen their sales,” said Warren Ellish, president and CEO of Ellish Marketing Group, LLC. “Communities keeping them out will obviously hurt them.”

Ellish suggested that the company might just walk away from places where it receives a chilly reception. “As a privately held company, they have the right to do that,” he said.

“They’ve been willing to give up one of seven days worth of sales,” he said, referring to the chain’s rule of keeping all its restaurants closed on Sundays. He added that executives might say, in effect, “If we miss a few markets where the brand’s not welcome, we’re no worse.”