Fast-growing chicken chain Chick-fil-A has long been known for sticking to its conservative roots. In a 2010 interview with Ad Age , an exec said the restaurant would sell hamburgers before it would consider opening on a Sunday. But what was once seen as an almost charming quirk of a Southern restaurant is increasingly coming under fire as the franchise funnels money into political causes that are seen as retrograde by large numbers of consumers once willing to give it a pass.

Things came to a head last week when an interview that Chick-fil-A President-Chief Operating Officer Dan Cathy did with the Baptist Press hit the internet.

In short, Mr. Cathy, son of founder S. Truett Cathy, affirmed the company's support of what he considers traditional marriage. "Guilty as charged," Mr. Cathy told the magazine. "We are very much supportive of the family -- the biblical definition of the family unit. We are a family-owned business, a family-led business, and we are married to our first wives."

Gay rights and marriage-equality activists, not surprisingly, were outraged by the statement, which illustrated the company's stance more explicitly than it had done before. Stuart Gaffney, media director with Marriage Equality USA, said that the quote was significant in that "he is connecting the dots, in case anybody had any doubt up until this week" about the company's view on marriage.

Not that critics had many doubts about where the company stood—they've been hammering it for donating to organizations such as the Family Research Council and Exodus International. "I think the dollars were speaking for themselves, and Dan Cathy confirmed they weren't just putting their money where their mouth is , but they were functioning as a mouthpiece for these anti-gay positions," said Mr. Gaffney.

But something about the latest round of criticism must have triggered an alarm. In an attempt to quell the critics, Chick-fil-A released a statement on its Facebook page Thursday that said, in part: "The Chick-fil-A culture and service tradition in our restaurants is to treat every person with honor, dignity and respect—regardless of their belief, race, creed, sexual orientation or gender. ... Going forward, our intent is to leave the policy debate over same-sex marriage to the government and political arena."

So it will march on with chicken sandwiches, cow commercials and football. Last year, the company spent $30.8 million in measured media, according to Kantar Media, sending its crowd-pleasing cows on a nationwide, hide-saving mission to get people to eat more chicken. Chick-fil-A's advertising is handled by Dallas-based Richards Group.

Chick-fil-A also sponsors the Chick-fil-A Bowl, a college-football championship that airs on Walt Disney Co.'s ESPN. Josh Krulewitz, spokesman for ESPN, declined to comment on the future of the Chick-fil-A Bowl airing on ESPN, saying only that "ESPN takes an inclusive approach in how we treat our employees and present our content."

Chick-fil-A knows how to woo national media despite not having a strong presence in the media capital of New York. The company has sent its marketing team to media companies, including Advertising Age, armed with plush cows and chicken sandwiches. But aside from the Facebook comment, the company has declined to comment or answer questions about whether it will continue to donate to groups opposed to gay marriage.

"Their donations speak louder than words," said Mr. Gaffney. "It's all fine and well to make a statement that they're leaving this to policy makers, but donations to groups that work actively against LGBT ... do harm to our community and actually are a critical part of the policy debate."

And those who are coming to the defense of Chick-fil-A may not do the chain any favors in the PR department. "Gay activists are not interested in debate," wrote Bryan Fischer, director of issue analysis for government and public policy at the American Family Association, last Thursday in a blog post on the pro-traditional-family's website. Calling gay-rights activists Big Gay, he continued, "They have a singular goal: to punish, silence, neutralize, marginalize and destroy anyone who defends the institution of natural marriage against deviant counterfeits. Hell hath no fury like a woman-who-thinks-she's-a-man scorned."