First, websites are websites. It doesn't matter if it's Facebook or your own personal blog, they're functionally identical in terms of features. They both have a means to communicate with other visitors and they're nominally accessible to the public at large with one being more popular than the other. Meaning that you're saying that if hypothetically a personal blog became popular then the blogger couldn't just delete posts they didn't like even though they're on the hook for hosting content (paying the host provider, laboring to write the content, laboring to moderate the content, and so forth). This seems suspicious to me since it treats being popular with being a monopoly which the two aren't the same. Facebook can ban you but you and your friends can freely setup a VPS with a web forum and keep it private among yourselves to talk and socialize. If say Comcast banned you then I would think you'd have an argument but with a website, it makes no sense in the context that you have an alternative to communicate with users but that you don't have a right to communicate via a specific application/platform.
Second, you're not owed a successful business model. This is important as you talk about folks making a living on websites like Facebook or YouTube (which is more relevant in my opinion). If the case law did bear out the opposite then any act of blocking spamming, scams, or other disruptive economic activity on websites would be illegal but it's not thankfully. I'd rather deal with having several websites not letting me post content because it isn't a good fit them (imagine Free Republic, who's banned me many years ago, letting me spread the good word of PJ Proudhon and other left market anarchists, or me forcing Rebel Media [a conservative website/outlet] to host a transgender vlog). Rather, it means we can self-sort into sites that fit our interests. Granny's knitting blog need not be bothered hosting posts about aquariums. Joe's betta fish web forum need not worry about hosting knitting content. And so on.
Third, no one is calling police on people being racists or fascists in general. This particular scenario is nonsense, so I'm going to just shrug and move on.
Fourth, many of those blocking tools you mention would be illegal under similarly proposed social media laws. All these current attempts to regulate popular websites are just another way to force users to consume content they would otherwise now (ex. trucks with pictures of aborted fetuses being driven around nominally pro-choice areas). The proponents of such regulations are against audiences self-sorting as they can't grow their support base. It's why so many other unrelated, but significant, laws are appearing such as laws forcing teachers to narc on LGBT students. It's meant to break down sites that have appeared to cater to such marginalized groups or are otherwise a big tent platform (inclusive to many but not for anti-social movements such as anti-LGBT). It's a multiprong approach to the demographic changes that has doomed reactionaries for the last three decades.
Just today he explicitly editorialized a post title (with a comment explaining why) because it exposed some government corruption; I don't even remember what because it was just so unremarkable and ordinary for HN. ETA: Oh lol it was the same subject as this post, but different title. I guess he let this one get away from him.
The article mentioned that 11 federal agencies were involved in asking social media companies to remove posts. I guess Hacker News needs standards mentioned in the FAQ about how many federal agencies need to be involved in an activity before it can be referred to as "vast".