We don't do that here
I'm finding it a little bit hard to believe that this needs to be said, but apparently it does. This is from Adam Serwer at Mother Jones:
Blocking construction of Chick-fil-a restaurants over Cathy's views is a violation of Cathy's First Amendment rights. Boston and Chicago have no more right to stop construction of Chick-fil-As based on an executive's anti-gay views than New York City would have had the right to block construction of an Islamic community center blocks away from Ground Zero. The government blocking a business from opening based on the owner's political views is a clear threat to everyone's freedom of speech—being unpopular doesn't mean you don't have rights. It's only by protecting the rights of those whose views we find odious that we can hope to secure them for ourselves.
The man has a right to make odious, bigoted remarks without the government threatening his business. You don't have to think too much about the implications of that for people who say ... Rick Perry doesn't agree with. Or Scott Walker.
Obviously, if private citizens would like to boycott Chick-fil-a over its owners beliefs, have at it. (I've been inclined to boycott it purely on the basis of its sub-literate brand name, but it's up to you.)There's nothing wrong with individuals exercising their right not to eat in a certain restaurant and asking other people to do the same. But the government refusing to allow the business to exist because of something the owner said? That's not how we do things in America.
As Adam says later in the piece, they will have to adhere to all the discrimination laws which, in both states where this is a controversy, applies to LGBT citizens. And there's no guarantee that people won't protest outside the business and agitate against them. That's all fair and constitutional. But if this fellow wants to open his business there and conduct himself within the laws of the state, the beliefs of the owner is none of the state's business.
Liberals are at a big disadvantage right now because so many more rich people are conservatives (and bigots, apparently) and they are donating vast sums to elect more Republicans. It's tempting to leverage whatever state power we have to fight it --- and there may even be legitimate ways to do that. But that's all the more reason to be vigilant about the Bill of Rights. It's a bulwark against what could happen if they are successful.