Harm isn't this subjective, there are objective criteria for classifying harm. Hate speech has no upside and causes much harm. That's not true of the others in your list.
You're begging the question here, assuming that what is called hate speech is necessarily harmful. I am quite certain that in the US political climate much of Palestinian political speech would easily be considered anti-semitic hate speech. Whether you consider this speech the valid outcry of the oppressed, or hateful bigotry of terrorist sympathizers, depends on your political perspective.
There is no definition of hate speech that is simultaneously objective and useful. If you can use it against your enemies today it can be used against you tomorrow.
Dan does a great job of moderation here, and if you break the rules repeatedly, you'll get kicked out. I guess that's "censorship" if you squint, but it's also YC protecting their private property and their rights to control who does what here. I don't see how that's a problem?
If that forum is censored with too broad a stroke, that actually harms society. I think everyone can agree that too broad censorship is bad, and if it hits large swathes of society, is really bad.
The difference between youtube and hacker-news is scale and near-monopoly. There is also an important difference of human and machine censorship. Not a difference of appeal, but a difference of unintended consequences. A human censor will notice when certain rules have unintended and too broad of an effect. There is a baseline of human oversight built in because there is a human somewhere. Automated systems do not have this property, if they have rules that seemed reasonable but aren't in practice, or aren't anymore, the system won't notice.
Like the other responder said. Youtube isn't just "someone's site". It is a full half of the bloody internet. The other half being split between Google and FB. I exaggerate for dramatic effect of course. But, most of the video content consumed online is currently on Youtube. And most of the internet is solely accessible through Google. Not to mention that a full 1/8th or 1/10th of the World has Facebook accounts. Funnily, I just Googled it, and according to the first hit Facebook has 2.2 Billion accounts.
At some point we have to admit/define/state that these entities and the products/platforms they provide are utilities for lack of a better word. Once they get to that point, they should rightly lose all ability to take sides. They must be hit with a giant stick if they so much as think of using their platforms to do anything other than make a profit. Imagine if telephone companies started dropping calls or disconnecting users that were saying "naughty" things.
No matter what someone is saying, banning them is a form of social signalling. It says, "we disagree with what these people are saying". There are many many things that the majority doesn't like the minority saying, and the world will be worse off if they manage to ban it all.
If I were gay, I would care less if people judged me based on their religion. I would care if a bunch of yokels started targeting me with violence.
But then, most hateful speech could predict a later killing. Someone who thinks gays should go to hell might decide to help them along, as it were. The difference between the two things you have quoted, then, is one of degree: saying the second demonstrates more hate than the first, but it is the same brand of hate.
But isn't the issue here precisely to ban illegal activities (sex trafficking adverts, hate speech)?
You might not care about these things, but censorship will eventually hit something you do care about. The impulse to improve society by controlling people's thoughts is never satisfied.
Can you now see why some of us have been consistently opposed to censorship generally, even when people were talking only about censoring the most disreputable people? We need to commit to equal treatment of all legal speech. The only alternative is suffocation.