I feel like this is a mild strawman? Like, the xkcd comic in specific is referring to the fact that claiming Free Speech rights under the 1st Amendment, which many people do, is not applicable to instances of, for example, Twitter banning one of its users, and it’s entirely correct in that. That’s why it specifies someone getting their show canceled (private organization’s choice) boycotted (free speech of others) or being banned from an internet community.
If we want to talk about the broader philosophical principle of free speech, then great, we can do that, and I think most people would agree that we need to be careful not to let the providers of communication services become the judges of what communication is allowed or not allowed.
But the right of private organizations to make decisions about their own services and set standards of behavior that they disallow should also not be infringed. Facebook, Reddit, Twitter, etc, all have standards of behavior that we (generally) agree with them censoring people for. When they decide to expand the list of behaviors they will censor, some will get very upset by this on general principle, but I’m okay with judging the action by the circumstance.
One of the major outcries around this was when Milo was banned from Twitter. But he was not banned for being a right wing talking head, or for saying controversial things. He was banned for witch hunting and whipping his followers up against an actress, including by posting a doctored image of her twitter that made it seem like she said something she did not. The fact that he’s also someone who constantly lies and says demeaning things about others is a happy benefit for those who find him an odious troll, but if Twitter cared about that they would have banned Trump years before he became president. There’s no evidence that the “tyranny of prevailing opinion” led to Milo’s twitter ban.
As the quotes in the post mention, we should be careful not to let the outcry of public opinion silence people as efficiently as a government would. But unless someone has the ability to ban individuals from the internet (and I’m pretty sure the Supreme Court ruled that such a thing is illegal, as far as the 1st Amendment is concerned), being banned from a particular platform does not seem to me to infringe on their rights, legal or philosophical, particularly if it’s for a specific reason that they clearly establish ahead of time is forbidden.