If you're not up to speed on the 'controversy' surrounding what Chick-fil-A does with its money, or some of the things Chick-fil-A President and COO Dan Cathy has said, Alvin McEwen of Holy Bullies has a pretty concise Q&A format rundown here.
When you get right down to it, it's not Chick-fil-A's actions that piss most of us off, it's the inaction of the media and of our allies that allow this sort of thing to persist. By all rights, Dan Cathy is an individual who has the right to say what he wants, and likewise as a private organization, what Chick-fil-A does with its money is its own business so long as it complies with the applicable laws.
But the media is euphemising what Chick-fil-A does, and in doing so letting them off the hook. Chick-fil-A is not donating to groups that "support traditional marriage," as the media has often reported, it is donating to groups that have spread scientifically disproven falsehoods about LGBT individuals in order to spread fear and keep them marginalized. It is donating to groups that not only endorse, but perform "conversion therapy," a widely discredited practice akin to psychological torture. It has donated to groups whose leaders have said that "homosexual behavior should be criminalized," and that "gays pose a danger to children."
When congress was drafting a resolution condemning Uganda's infamous anti-LGBT laws which call for the death penalty for LGBT individuals, there was a religious organization that said, "don't do that." Chick-fil-A gives money to that organization. Repeat: Chick-fil-A gives money to an organization that doesn't think the murder of LGBT individuals is worthy of condemnation.
But let me be clear, while I think what Chick-fil-A does is reprehensible, this is not about them. This is about the LGBT allies that give them money and let them do it. It's about those that sate their own lazy grip on morality by saying things like, "well I don't agree with them, but their chicken is good, haha." I don't want to be too harsh here, because yelling at people is a pretty poor way to get them on your side, but I feel like I need to remind them of something. We are a minority. While there are many of us, we are still far outstripped by straight individuals. As such, we need your help. That includes standing up for us when you are able. Real standing up, not 'watching a bully beat the hell out of some nerdy kid and then condemning him after' standing up. Eating a three dollar chicken sandwich from a fast food restaurant means more to you than showing support for your friends and neighbors? Really?