The Georgia-based chain, whose CEO infamously attacked marriage equality in 2012, has scored a zero in the Human Rights Campaign's annual buyers guide for its past antigay giving and its lack of protections for LGBTQ employees.
Buttigieg -- the mayor of South Bend, Ind., who has launched an exploratory committee for a presidential campaign, but has not officially announced one -- stressed the importance of finding the ties that bind between people of different viewpoints in his conversation with The Breakfast Club.
"We've got to find a way to use our identities to reach other people," Buttigieg said. "What can we talk about that brings us together? Because I have no clue what it's like to walk in the shoes of so many other people. But I can talk about some of the pieces of what I carry with me and see if it rhymes with their life experience."
"Good art has that. Good music has that. Good literature has that," he said.
"Good chicken sandwiches," added cohost Charlamagne tha God.
Buttigieg is a rising star among the Democratic contenders for the presidency. A recent Iowa Caucus poll placed Buttigieg in third place within a crowded field. With 11 percent support, Buttigieg trailed only former Vice President Joe Biden, at 25 percent, and Vermont Sen. Bernie Sanders, at 24 percent.
Buttigieg also recently spoke with The Advocate about his gay identity -- and what he would tell critics who believe he is too "heteronormative" at a recent West Hollywood town hall. "I realized early on in my life that I was different," he said. "It took me a very long time to acknowledge who I was even to myself, let alone to others. But I am who I am and I'm proud of who I am. And I want to acknowledge and support everyone else who is coming to terms with who they are."
"I don't know if it makes sense to ask questions about how gay is gay enough," the presidential hopeful continued. "All I know is that I'm gonna be true to myself and hope everyone else is empowered to do the same."
Watch his interview with The Breakfast Club below.