"Well actually, the first amendment only protects against government intruding on free speech, it doesn't apply to the rest of us!"
Free speech used to be the thing everyone agreed on. It's like a fundamental tenant of Western, liberal democracy has gone out of vogue.
https://en.wikipedia.org/wiki/First_Amendment_to_the_United_...
The fact many supporters of this guy's firing are treating these principles as technicalities is troubling. The first amendment is a starting point, not a loophole.
So the "free speech only applies to the government" or the "free speech doesn't mean you can say whatever you want without consequences" argument is really just a reflex to "free speech" being often misused.
But in this case - I agree with you. The knee jerk calls for the guy to be fired without really hearing him out or engaging substantively on the issues like censorship and an affront the free exchange of ideas upon which democracy depends.