A Southern-fried chicken sandwich on a soft white bun with a couple of pickle slices is fast becoming the culinary symbol of one of the country's major social issues.

The Baptist family that owns Chick-fil-A, an Atlanta-based fast-food chain with stores in 38 states and the District of Columbia, for years has given millions of dollars to groups fighting same-sex marriage and supporting heterosexual ones.

Small protests against its position have swelled and receded in the past couple of years, but the battle recently has spilled into the halls of city governments and the presidential campaign. Even the Muppets are involved.

The latest uproar began this month when Dan Cathy, whose deeply religious father, S. Truett Cathy, started the company in 1967, told a Christian news organization that Chick-fil-A supported "the biblical definition of the family unit."

Cathy, the company's president and chief operating officer, said later in a radio interview: "As it relates to society in general, I think we are inviting God's judgment on our nation when we shake our fist at Him and say, 'We know better than you as to what constitutes a marriage.' "

The statements, which prompted groups such as the National Organization for Marriage to call Cathy a corporate hero, echo an ethos the company never has hidden.

In early 2011, a Chick-fil-A restaurant in Pennsylvania donated food to a marriage seminar conducted by one of that state's most outspoken groups against homosexuality.

Advocates on both sides weighed in, and students at some universities began trying to have the chain removed from campuses.

Equality Matters, an online investigative organization dedicated to gay and lesbian issues, last year obtained tax records that showed the company's operators, its WinShape Foundation and the Cathy family had given millions of dollars to groups whose work includes defeating same-sex marriage initiatives and providing therapy intended to change people's sexual orientation.

So Cathy's statements might have passed without much notice except that Carly McGehee, a New Yorker, decided to stage a same-sex kiss-in on Aug. 3, urging gays and lesbians to show up at the company's 1,600 restaurants across the country in protest.

That moved Mike Huckabee, the former Arkansas governor and Fox News commentator, to declare Aug. 1 as Chick-fil-A Appreciation Day. His call to action, which he posted on Facebook last week, garnered such a response that it tripped the site's spam filters, and the page was taken down briefly Tuesday.

Rick Santorum, a former Republican presidential candidate, has jumped in. On Wednesday, he rallied his 200,000 Twitter followers: "With two of my boys, Enjoying chick-in-strips and an awesome peach shake at Chick-fil-A. See you here next Wednesday!"

On the other side, Alderman Proco Moreno of Chicago said this week that he would not move forward on land-use legislation that the company needs to open a second restaurant in that city, and Boston Mayor Thomas Menino last week sent a letter telling Cathy that his company was not welcome there.

The Jim Henson Co., which created toys for the chain, will not offer any more Muppets. On Friday, the company said Chief Executive Lisa Henson supports same-sex marriage and would donate money that the company had received from Chick-fil-A to the Gay and Lesbian Alliance Against Defamation.

About the same time, Chick-fil-A posted signs announcing a "voluntary recall" of all Jim Henson's Creature Shop Puppet Kids Meal toys, citing reports that some children's fingers had gotten stuck in the holes of the puppets. Last week, Cathy said his company would "leave the policy debate over same-sex marriage to the government and political arena."

People aligned with the Cathy family's position have said they have visited the chain more frequently since its involvement in the issue became more widely known. Others, such as Jeff Graham, executive director of the gay-rights group Georgia Equality, say they are not sure this protest will be any more successful than previous efforts, which fizzled.

Graham said he was more interested in encouraging the company to write an anti-discrimination policy that includes gays and lesbians.

And he did not know, he said, if he will show up for the kiss-in. If he does, he certainly will not order a sandwich.

"Frankly, I'm a vegetarian, and it's been 20 years since I ate there," he said.