But the first amendment says that government can't take away your right to free speech....
The First Amendment says that
Congress can't take away your right to free speech.
Of course, people always bring up the shouting fire in a crowded theater argument...
Per the First Amendment, Congress cannot take away your right to shout 'FIRE!' in a crowded theater. But the First Amendment doesn't apply to State and Local governments, which is why State and local governments decided to make it illegal to shout 'FIRE' in crowded theaters.
As for non-government entities, one always has the right to speak freely. However, there may (and will be) consequences to exercising that freedom. Want to cuss out your boss in front of all your peers? Yes, you have the right to do that. But your boss has the right to fire you for it.