Everyone understands that the First Amendment restrains only government actions, not social pressures being brought to bear. There is an allied question, however, about those social pressures. The First Amendment uses government itself to restrain government from interfering with free expression. The People, insofar as they are properly thought of as acting through the state, are therefore using an aspect of their common will to restrain itself.
Why shouldn't social pressures be brought to bear against social pressures in the same way? If a group attempts to use social pressure to get someone fired for saying things they find objectionable, shouldn't those people themselves be pursued (and their employers subject to demands that they be fired at once)?
That sounds like a pretty unpleasant place to live. Those calling for civility are doubtless thinking of that. I wonder if the proper analogy, though, isn't to nuclear war. Mutually-Assured Destruction proved an effective restraint, just because a post-war world would have been such an unpleasant place to live.
In the current moment we see not only organizations but ad-hoc movements engaged in a sort of blood-lust, in love with the unrestrained power to destroy. There is no legal recourse against them, because the government only properly restrains the government. It is society that must restrain society.
I yield to none in my respect for courtesy. Certainly I have no desire to live in the kind of world in which our every expression is carefully watched by our ideological enemies in the hope that some public expression of religion, some joke, some interview should produce an opportunity to destroy our lives.
There are only two roads to avoid that world, though, and the first road is to avoid all public expressions of religion, all jokes, or the giving of interviews. The other is to make clear that this is a two-way street, if they insist upon it. Hopefully the cataclysm can be avoided, but clearly it will not be avoided out of the plain goodness of peoples' hearts.