I'll start off with a disclaimer that the comments below are my interpretation of the rules, but other staff may have different ones. Moderation is a team effort and we often discuss borderline cases and reach a consensus over time.
I'll start off on a general note. Under the new rule, it can apply both to common protected classes like race, gender, religion, etc, as well as other groups like political parties, activist movements, ideologies, etc. The former group is more likely to be classified as hate speech, while the latter is more likely to be group slurs. The former will, on average, be a more serious offence, but the latter is still a violation because it's not constructive to the conversation. If you say "Republicans are all evil" or "Anyone who voted for Hillary Clinton is an idiot", that's not going to do anything to advance whatever argument you're making, will offend other forum members, and will likely take the discussion off topic. Many of these sorts of comments were already covered by other rules, so there's not a significant change here, but more a clarification.
Now, to your specific example. There are probably contexts where it's appropriate to post your opinion on this. But, I would imagine that the majority of contexts would fall under this rule (and previously, other rules in the majority of those). A couple of factors to take into account are a) the term hate group has a specific meaning, that does vary slightly by source, but generally refers to promotion of hostility or violence against other classes of people, where those classes are defined by immutable characteristics such as gender, race, sexual orientation, etc; and b) it's a highly emotive term. The combination of these mean that applying it to a group that doesn't meet the generally accepted definition, or does so only at a stretch, is likely to be contentious and offensive to some. On the other hand, applying it to a group that clearly meets the criteria, such as the KKK, would be fine. Another factor would be why the comment is being made. In most cases, you could make the same argument you're trying to make without comments that are likely to offend others or take the conversation off topic. If the topic itself was about whether a group could or should be classified as a hate group, then it would be on topic, and potentially legitimate to post your opinion there if it advanced the conversation, but - as always - depending on the exact context and how your opinion is expressed.
Again, the context is important, but as a general topic I don't see a problem with this per se - there's legitimate viewpoints on both sides. Making slurs against transgender people within that thread, would, of course, be a violation of the rules.
The inclusion of the words "that a reasonable person would find offensive" in the new rule is quite deliberate. "Reasonable person" is a legal term with a specific meaning. We've included it to show that common sense applies. A single person being offended doesn't mean that your post violates the rules; conversely, your post can violate the rules without everyone or even a majority finding it offensive.
Hope that clarifies things!
