My gut feeling is that this is a merely a leftist website designed to manipulate public opinion.
In fact, everyone I have met and talked with about the Chick-Fil-A issue has come down on the side of the restaurant. As a teacher, I have a direct line to liberal, leftist, young, and sometimes clueless opinion, and the responses I'm hearing are all on the side of the restaurant, ranging from ho-hum who cares to folks actively seeking a Chick-Fil-A to eat there. No one suggests activism, protests, things like that.
Here's a photo from a former student posted on Facebook - a blue-blood liberal most of the time - showing what seems to be the real opinion of most people. I agree that the poster misrepresents the Chick-Fil-A position, too - but it also represents an overall disgust of the leftist position. (Hope the link works!)
Methodology:
These brands were rated using YouGov BrandIndexs Buzz score which asks respondents, "If you've heard anything about the brand in the last two weeks, through advertising, news or word of mouth, was it positive or negative?"
So this is not a measure of opinion of the brand, but the frequency of the talk from others. Hardly an indicator of popularity with the respondents.