> That Colorado baker didn't want to effectively participate in their wedding ceremony which he was opposed to

You've missed the crucial point, namely that not every discrimination against minorities is on a par and not every minority needs to be or should be protected. I've seen this flawed rhetoric used recently by by the "alt right" Nazi movement, who love to turn arguments around because they are essentially cruel and trolling. These are not good arguments, though, and you shouldn't fall for them.

The right answer to these fake arguments is to say "no."

No, ISIS sympathizers, Nazis, Stalinists, or pedophiles do not have a right to be protected as minorities exactly on a par with gay couples, catholics, or divorced mothers with three children. If a minority incites to crimes or violence or does not follow basic principles of civil discourse, then they are not going to be protected and there is no need to be tolerant towards the intolerant.

What the baker did was wrong because gay couples are not a violent hate group. It was wrong, as an action, independently of the baker's personal opinions. Gay couples are de facto not a violent hate group or criminals, and at the same time there are many reasons why they should be protected as a minority. When taking a look at examples like the baker case, you need to also bear in mind that someone can be a racist, antisemite, misogynist, and so on, without knowing that he/she is one. In fact, that's the most common case. You should also take into account that every working democracy has a duty to protect minorities in order to prevent a "dictatorship of the majority." The protection of minorities is a building block of democracy, not a DLC add-on.

> If that were the case, they'd be quite happy with optional personal filters.

You're talking about the private motives of forum participants, but these have no substantial bearing on what these companies and private site owners do. While I'm personally fine with ignore functions and you can already do that on Reddit, it is widely accepted that this is not a general solution, because the filters only work for yourself. That means that the whole world will see the replies by toxic users to your own posts. That means that all forums will look, for the outside observer, as if the worst scum of the earth and all obvious trolls had "won" every argument. Of course, people find this idea unpleasant. I understand that very well, even though I'm personally fine with kill files like on Usenet. The problem is that nobody wants to join such a forum, once a certain threshold is reached, only trolls and extremists will find it appealing. Kill files don't help against this effect, which in the end will destroy your forum.

The primary motive of companies and private forum owners for bans and post removals are thus proper and perfectly normal. Civil discourse has rules and these are enforced everywhere. There is no substantial difference between online and real life discourse in that regard and there shouldn't be one. Forum owners have all right of the world to ban hate groups and toxic users and you still haven't explained why they shouldn't have this right. It's their forums.

> But nobody is calling for that because what they really want is to prevent 3rd parties from being influenced by ideas that they don't agree with.

Everybody wants to do that, including all extremist groups on earth. It would be irrational - or at least, pragmatically incoherent - not to have this desire. But again, I don't think that's the reason why companies ban forums and remove posts. Their main goal is to keep sites usable and pleasant enough for their user base to go there. There are plenty of examples of forums that completely failed, because they didn't moderate heavily, and one of the reasons why HN is so good is the heavy moderation.

Apart from keeping the forums usable for the general target audience, there is another, more mundane reason for bans and post removals, of course. Some of the banned subreddit were questionable under US law and downright illegal under other jurisdictions, and Reddit could have gotten into serious legal trouble in other countries if they didn't ban these. The same holds for companies like Google and Facebook.

For example, displaying Nazi symbols and Nazi propaganda or supporting Nazi or terrorist groups is illegal in Germany, and German authorities can ask for the immediate removal of posts and forums dedicated to such activities. If companies like Reddit, Google, or Facebook wouldn't comply, they could be forced to close down access to their websites in Germany, and they don't want to do that, because Nazis are not their target audience. You may think about these laws whatever you want - they were passed after WW2 under strong influence from the US -, but the reality is that they exist and companies have legal advisers that check for compliance.