Square CEO Jack Dorsey sparked a backlash on Twitter over the weekend. (Richard Drew/AP Photo)

If any CEO knows how quickly a social media debate can erupt over a politicized brand like Chick-fil-A, it ought to be Twitter and Square CEO Jack Dorsey.

Yet Dorsey still found himself on the receiving end of an online backlash to a tweet -- and a later response -- he fired off this weekend while promoting a feature of one of his companies' products. After tweeting a screenshot of a Chick-fil-A "boost," or cash back received by using a debit card from his mobile payment service, Square, some Twitter users noted how the fast-food chain, which closes on Sundays, has been associated with conservative causes. Back in 2012, Chick-fil-A CEO Dan Cathy made remarks supporting what he called the "biblical definition" of family and gay-rights activists have been critical of the company's foundation's giving in the past.

Starfish Media CEO and former CNN anchor Soledad O'Brien tweeted "this is an interesting company to boost during Pride month, @jack." Others joined in with tweets calling for Dorsey to "delete this or follow up with how much free advertising you're going to give GLAAD," the advocacy group, or asking "I wonder how LGBTQ employees of Twitter feel about this post?"

But O'Brien's tweet prompted a statement of regret from Dorsey, who wrote "you're right. Completely forgot about their background," which only fueled the backlash further. Now critics were not only blasting the timing of his tweet amid Gay Pride Month but defending Chick-fil-A's service, food and values. Wrote one user: "Their background. You mean a company that stands by its Christian values? Or a company that employs over 40,000 people? How about a company that gives scholarships to its employees? Stop with all this liberal ridiculousness. You enjoyed their food. Period." Another admonished Dorsey to "relax, Jack it's just a sandwich."

The brouhaha is a reminder of how quickly CEOs' comments on social media can become politicized, even if unintentionally, and the vigilance CEOs must use when weighing in on anything that might even remotely touch a political nerve.

"As a public figure I think you should always be having that voice on your shoulder saying 'who am I going to aggravate or annoy or irritate today?' " said Leslie Gaines-Ross, the chief reputation strategist at Weber Shandwick. "You have to be on guard, especially when you're a CEO."

Gaines-Ross said that in today's environment it's more difficult than ever to remain neutral, and that "if you dig deep enough, you can find something that will put a brand on either side" of the political divide. "Most everybody is working hard to line up which are red brands and which are blue brands."

A spokeswoman for Twitter pointed to Dorsey's response to O'Brien and declined to comment further. An e-mail to Square and Chick-fil-A were not immediately returned. After the 2012 controversy sparked by Cathy's remark, the company said in a statement that it would "leave the policy debate over same-sex marriage to the government and political arena" and that its culture is "to treat every person with honor, dignity and respect – regardless of their belief, race, creed, sexual orientation or gender." Cathy has since called his remarks a mistake, and reports say the fast-growing company has worked to broaden its brand image away from controversial issues as it has expanded into cities like New York and tried to cater more to millennials.

Some consumers, as judged by the backlash to Dorsey's comments show, still connect the brand with such issues, questioning Dorsey's move. Others may have thought the implication of Dorsey's tweet was that he was "boosting" Chick-fil-A, when he appeared to be promoting the "boost" or cash back received when using Square's Cash app debit card. "Back to the part where @jack is boosting a notoriously anti-LGBTQ company in the middle of #Pride month," wrote one user.

Others, however, applauded Chick-fil-A's service ethos, noted its reputation as a good employer. Some also tweeted links to an article written by a campus gay rights activist about the "respectful, enduring communication and built trust" between he and Cathy in recent years and complained about the hyper-politicization of today's world.

"Oh, grow a pair, Jack. The food is good," wrote one user. "Not everything is about politics or religion or someone else's overly sensitive feelings."

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Getting a Chick-fil-A franchise is harder than getting into Harvard

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