Free speech is important even in contexts where the First Amendment doesn't apply. The First Amendment is important because free speech is important, not the other way around.
I agree with this:
You can say whatever you want: you should also expect
to take heat from non-like minded people.
But I think this misrepresents the view of free speech advocates (it certainly misrepresents my viewpoint):
At some point the free speech concept transitioned to
"I should be able to say whatever I want with no
consequences".
On the contrary, I think a lot of left-authoritarians who want to censor right-leaning speech are the ones touting this viewpoint. It's not the pro-free-speech crowd that wants no consequences for what they say, it's the anti-free-speech crowd. One of the consequences of stating your opinion publicly is that people will disagree with you.