I don't like where this argument goes. Do you think it should be legal for Google to remove every search result of a cannabis business? Should it have been legal for Google to censer anyone advocating for LGBT rights before they were a protected class? If you answer no to those questions its hard to justify saying that 1A only applies to the government.
That's not a statement that I think either of those things is right. I would and should expect a lot of user and community backlash from actions like those.
But as far as the law is concerned, those things should be legal. Again, because to do otherwise would mean forcing businesses to adopt the government's position on any number of subjects.
And no, I'm not a free-market libertarian. There are lots of things I think businesses should be forced to do under strong regulatory terms. This just doesn't happen to be one of them.