On the one hand, Chick-Fil-A is gross, and probably on the wrong side of history. On the other hand, Mr. Chicken Filla can say whatever he wants, it is still a free country, somehow. Just because he's a bigoted jackanape doesn't mean he shouldn't get to dig himself into a gigantic, bigoted stupid hole with his words.
Free speech does not mean only your speech is free. Yes, you are free to boycott a fast "food" chicken frying place. He's also free to do what he wants with the business, including denigrating a significant portion of the population at his peril. Calling for the ban/burning down/shutdown of his restaurants only hoists him up like a martyr.
In short, don't eat at fast food joints and you won't have this problem.