I am not going to address many of your questions because the answers are obvious if you honestly think about them (an honest reading of the rhetoric should supply all the necessary clues); also, I'm not familiar with the details (though it's still obvious what's going on). I do, however, want to provide some historical background about hate groups in response to:
> Then why were these 'hate groups' active before the allegations were made, if they all truly only target people for "who they are" and not "what they do"?
(I assume you meant "weren't", right?) Well, history teaches us that oftentimes there's a lot of pent-up anger in people that only rises to the surface -- in the form of mob violence -- in response to a trigger, which takes the form of an accusation of some illicit action taken by the mob's victims. For example, many pogroms against Jews were incited by some incident[1][2] (usually fabricated, sometimes partly true, sometimes blown out of proportion). Same goes for lynch mobs in the US. That's just how mob violence works.
Also -- and this is very obvious, but I think I'll be amiss if I don't explain this point, you say:
> while conveniently ignoring the harassment other GG members receive from anti-GG ones?
You imply symmetry where there is none. In civilized society, it's perfectly acceptable to harass members of hate groups. In fact, it's a civic duty to do so. The KKK and the SPLC are not two equal-but-opposing sides. The former is a hate group while the latter isn't. When one harasses the other it's mob violence; if it's the other way around it's common sense.
Also, the "harassment" against members of the hate group (although, again, I'm not familiar with the details of this seventh-grade kerfuffle) is often just calling them out for what they are. While clearly moronic villains, unlike in comic books, they don't appreciate and accept their villainy because they're morons. In their delusions they are misunderstood mavericks, and calling them out for the idiot brutes that they are makes them feel harassed, when, in fact, it's just that their behavior has no place in sane human society.
And before you cry out, "I'm just a nonconformist with unpopular opinions, and the majority calls me a hate group because their PC minds can't stand original thought" let me give you a little advice. If you have two sparring groups, it's quite easy to tell which is the hate group baddies and who are the goodies -- and it has nothing to do with the majority. If one group has too many people you wouldn't want your daughter to date -- that's the hate group[3]. And if many sane people tell you you're part of a hate group, before arguing with them, try to think very hard if they may be right, because they probably are. Another tell: if a group refers to social justice as a negative -- they're the bad guys.
[1]: https://en.wikipedia.org/wiki/Pogrom
[2]: https://en.wikipedia.org/wiki/Krak%C3%B3w_pogrom
[3]: If you think about half the population would be fine with their daughter dating people in one group and half with the other, then you may have a simple case of two opposing political movements.