So why is it OK for you to voice your opinion about the group but its not OK for them to voice their opinion?
I'm just stumbling through this thread, so I might be missing posts after this one. But this post touches on what I see as a very common misunderstanding, and it crops up around here all the time. People are perfectly entitled to hold whatever opinion they'd like, even if it's despicable.
However, when you voice an opinion, you are going to get a reaction of some kind, whether positive or negative, and if it's hate speech or something offensive, you might be inviting some kind of reprisals.
What seems to have happened here, though, takes that one step further, where a group is attempt to exert influence over a situation based on their opinion and THAT'S where you end up experiencing a lot of push back. This happens all the time. A group will try to boycott another group and then try to say, 'Well, I'm only voicing my opinion.' Well, no, you're not. You're trying to change other peoples' behavior so that it conforms to your opinion, and it's reasonable to expect some kind of opposition.
And as with all things human nature, the more extreme your position, the more vehement the opposition.
I personally don't like statements such as, "Yeah, well, the reason I can voice my opinion is that mine isn't hate speech/evil/wrong/stupid/whatever." This is the other side of the same coin. You are welcome to voice your opinion and I'm perfectly okay sharing my opinion, that you're an idiot. ("you" in general, not anyone specific here)