That's true to an extent (and so is what ativzzz says, so you're both right). But the reasons for what you're talking about are much misunderstood. Yishan does a good job of going into some of them in the OP, by the way.
People always reach immediately for the conclusion that their controversial comments are getting moderated because people dislike their opinion—either because of groupthink in the community or because the admins are hostile to their views. Most of the time, though, they've larded their comments pre-emptively with some sort of hostility, snark, name-calling, or other aggression—no doubt because they expect to be opposed and want to make it clear they already know that, don't care what the sheeple think, and so on.
The way the group and/or the admins respond to those comments is often a product of those secondary mixins. Forgive the gross analogy, but it's as if someone serves a shit milkshake and when it's rejected, say, "you just hate dairy products" or "this community is so biased against milkshakes".
If you start instead from the principle that the value of a comment is the expected value of the subthread it forms the root of [1], then a commenter is responsible for the effects of their comments [2] – at least the predictable ones. From that it follows that there's a greater burden on the commenter who's expressing a contrarian view [3]. The more contrarian the view—the further it falls outside the community's tolerance—the more responsibility that commenter has for not triggering degenerative effects like flamewars.
This may be counterintuitive, because we're used to thinking in terms of atomic individual responsibility, but it's a model that actually works. Threads are molecules, not atoms—they're a cocreation, like one of those drawing games where each person fills in part of a shared picture [4], or like a dance—people respond to the other's movements. A good dancer takes the others into account.
It may be unfair that the one with a contrarian view is more responsible for what happens—especially because they're already under greater pressure than the one whose views agree with the surround. But fair or not, it's the way communication works. If you're trying to deliver challenging information to someone, you have to take that person into account—you have to regulate what you say by what the listener is capable to hear and to tolerate. Otherwise you're predictably going to dysregulate them and ruin the conversation.
Contrarian commenters usually do the opposite of this—they express their contrarian opinion in a deliberately aggressive and uncompromising way, probably because (I'm repeating myself sorry) they expect to be rejected anyhow, and it's safer to be inside the armor of "you people can't handle the truth!" than it is to really communicate, i.e. to connect and relate.
This model is the last thing that most contrarian-opinion commenters want to adopt, because it's hard and risky, and because usually they have pre-existing hurt feelings from being battered repeatedly with majoritarian opinions already (especially the case when identity is at issue, such as being from a minority population along some axis). But it's the one that actually has a hope of working, and is by far the best solution I know of to the problem of unconventional opinions in groups.
Are there some views which are so far beyond the community's tolerance that any mention in any form will immediately blow up the thread, making the above model impossible? Yes, but they're rare and extreme and not usually the thing people have in mind. I think it's better to stick to the 95% or 99% case when having this discussion.
[1] https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...
[2] https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...
[3] https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
[4[ https://news.ycombinator.com/item?id=6813226