You have to be careful not to gloss over some extremely important distinctions:

1a) People speaking out against Chick-Fil-A, even people in office? Ok.

1b) People not spending money at Chick-Fil-A because of this? Ok.

1c) Government officials banning Chick-Fil-A? Absolutely not. Even the ACLU has come out in support of the CEO against the threatened bans.

2a) Speaking out against something, even an existing law? Ok. In fact, being able to speak out against laws that you think are wrong is one of the main major reasons for having a First Amendment.

2b) A CEO of a private company saying he opposes same-sex marriage, even if he outright says the laws are wrong, and a majority of people thinks that's a stupid opinion to have? Ok (he's wrong but legally ok).

2c) Having discriminatory practices in place (officially or even unofficially)? Not ok. However, no one has claimed that Chick-Fil-A actually engages in discriminatory practices. Only their CEO is wrong-headed and intolerant. That is a HUGE distinction.

So, sure you can lose clients and sales over your views. You could even have the Mayor of Chicago call you a jerk and say you don't belong in the city. But once it crosses over to "and you have such jerky views that I'm going to use my zoning authority to prevent you from being in my city", it has crossed the line into a First Amendment violation regardless of whether your views oppose existing laws, regardless of whether you are public or privately owned. It is wrong.

I found these expressed and informed my ideas quite well:
https://www.salon.com/2012/07/26/rahm_emanuels_free_speech_attack/

https://www.cnn.com/2012/07/30/opinion/randazza-first-amendment/index.html

So, I suppose it is simple:

1) You can say dumb things.
2) Your business can be called out and lose sales over that.
3) But the government cannot use it's authority against you unless you actually violate the law.