I hope you don't get any hate either, because it would be dumb to hate you for having a perfectly reasonable opinion.
It's misinformed however.
Gamergate is extremely important to the culture of video games and the internet as a whole. They're a highly organized and entrenched community of shit heads who represent a new way forward for this kind of fuckery. The abuse faced by those who've been targeted is very real, much more extreme and focused, and hasn't been propped up by anything but the development, production, and enthusiast video game community's lack of will toward vehemently denying everything it stands for.
I'm not saying that the consequences of their actions don't matter. Of course they do. Anyone who makes genuine threats to another person, online or offline, should be prosecuted to the fullest extent of the law, no doubt about that.
What I am saying however is that GamerGate should not be given a platform, by which their actions are highlighted and broadcasted, in the same way that school shooters should not be featured and named on TV. Threats should be taken care of through the police, communities should come together to prevent such harassment and then people should move on and work on building stronger, better communities where such hatred is not tolerated.
And again, I think that GamerGate represents nobody but themselves. Their goal is mostly to get attention and anger as many people as they can, and thus consistently having the same conversations about them serves no point but to give them attention. I can name many deeply entrenched communities, such as Nazi's, racists, and religious and political extremism, that are organized and annoying, but those groups also don't represent an entire culture or require a consistent conversation about them specifically. That doesn't mean you should ignore the problem, it just means you shouldn't broadcast their thoughts or ideas, or twitter and facebook handles. You can talk about racism, homophobia or extremism without giving people with names unneeded attention.
All I'm saying is, let's have that broader conversation that you mentioned. Let's stop posting screenshots full of twitter handles or chan threads, let's stop keeping them in the eye of the mainstream and instead let's shift towards an actual conversation, where GamerGate doesn't get to be mentioned and given attention or clicks. And again, let's also stop this notion that videogames = misogyny. That is not the way to start a conversation, that is a way to demonize an entire creative industry over some shitheads on chans and twitter.