The First Amendment is perhaps the most powerful manifestation of the philosophy of free speech in our world today. As a result, we have a habit of conflating the two. But a culture of free speech can wither while the First Amendment remains strong (and vice versa).
What steams my clams is that the people who complain about private forums exercising editorial discretion tend to be the same people who insist that private property rights are sacrosanct, and so, for example, private property owners should be able to ban union organizers from their property [1]. This strikes me as brazenly hypocritical. Either free speech trumps private property, or private property trumps free speech. You can't have it both ways.
[1] https://www.natlawreview.com/article/supreme-court-holds-uni...
They are not, they just aren't so unequivocally bad that you can ban them in the constitution with a single sentence.