We are not helping bigots promote their cause by calling them out; we are helping defuse it. We are making it known that it's not morally acceptable to say these things. Look at every social justice movement throughout history. We haven't progressed by ignoring hate and staying silent.
I wrote to Sia on Twitter and expressed my disappointment. I wasn't expecting a reply, but, to my surprise, she responded and thoughtfully listened, and we proceeded to have a lengthy (by Twitter standards) conversation.
When people -- especially the politically jejune -- see "cool" anarchist groups like Anonymous using language that is the very definition of hate speech, won't the assumption be that it's OK to use it? It's not. And claiming these words aren't offensive is itself offensive.
Usually hate speech is pretty direct. A good example is the Web address for the Westboro Baptist Church. But sometimes hate speech isn't direct at all. It may even be a little bit involved. Consider, for example, how anti-LGBTQ organizations use the word "family."
As a parent, one of the great joys is exposing my kids to all the stuff I liked when I was little. We have a built-in excuse to buy things like The Goonies or The NeverEnding Story. But a few times that we've gone back to our childhood favorites, we've had a harsh wake-up call.
Denying basic civil rights is hate. Characterizing an entire group of people as sick is hate. When people express these beliefs or vote for those who do, they are encouraging those who waves signs, throw slurs, and worse. And they are killing children.