I won't post links to examples here because, again, that is probably not within the site guidelines. But I'm happy to supply on request.
Outside that extreme sort of comment, though, the problem is not as simple as it sounds, or feels, because there's no consensus on how to define or interpret these terms. That means any particular moderation call is going to end up feeling wrong to a sizeable subset of users—good-faith users, not bigots or trolls. Put a few of those data points together and pretty much every reader is going to find a pattern to dislike. It's literally impossible to avoid this, even if we could see everything.
One consequence is that we/I regularly get lambasted with every horrible label that exists in polite society (a clarifying example: https://news.ycombinator.com/item?id=22941387), because most people misinterpret a sequence of bad-data-point experiences to mean "the mods must agree with and support this kind of thing".
I wish I could get across to people how these perceptions are unavoidable given the stochastics of the site (HN is a statistical cloud) and how our brains deal with randomness (by strongly overinterpreting it). I've been writing about this for years - a lot of which shows up in these links: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... and https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... - but it doesn't really land. Even if one knows these things intellectually, it doesn't change how they feel, and the feeling determines everything.
Joe Biden could point out, correctly, that he'll receive criticism both from the left and the right whatever choices he makes. But so what? It doesn't follow from this that he's actually making the right decisions, or that he's found some kind of perfect middle way, or that he doesn't have any discernible political leanings. Nor does it follow that anyone who thinks that Joe Biden is left (or right) of center has been deceived by some kind of statistical artefact or cognitive illusion – though no doubt some of them may have been.
So I'm not sure that I buy the claim that HN is striking the roughly the right balance because roughly as many people call you a Commie as call you a Nazi. I mean, who cares what people hurling thoughtless insults think? Since when were they the instrument by which we calibrate the range of acceptable discourse?
One possibly constructive suggestion. It might help if there was some kind of explicit indication that an account had been banned. It would be reassuring to see this when stumbling across some horrible post from a negative karma account. I bet a lot of these accounts have been banned, but there's no visible indication of that.