I don't understand the boycott of a franchise, you aren't hurting the Cathy's, only the franchise owner and his employees. Perhaps if you manage to actually close the local restaurant you might put a small ding in their bottom line from a lost franchise fee, but really you are just screwing over the franchise owner and employees, who are actual members of your community, trying to make a living.
Your own article says that they are donating to different charities, so it looks like they will not be supporting the charities that everyone has a problem with. So are you waiting for Mr. Cathy to come forward and embrace the LGBTQ+ community in order to be ok with the restaurant? You really want him to lie just so you feel ok about a chicken sandwich?
Chick-Fil-A is a place with good food and great service, and no matter which one I've been to in any location in America, I always get good food and great service. How many other fast food chains can you say that about?
You are free to boycott them all you want of course, that is the beauty of the country we live in. But if a Christian owned business can't set up shop at a Christian university because of the Christian beliefs of the owners, I would find that to be quite odd.