Twitch just shot themselves in the foot.
I don't know how much the rest of you know about internet gaming culture (I'm an expert), but honor and shame are huge parts of it. It's not like it is on Youtube where you can become successful by being an asshole. If you screw someone over on the internet, you bring shame to yourself, and the only way to get rid of that shame is repentance.
What this means is the gaming public, after hearing about this, is not going to want to partner with Twitch for sponsorship, nor will they stream any of Twitch's games. This is HUGE. You can laugh all you want, but Twitch has alienated an entire market with this move.
Twitch, publicly apologize and cancel this content muting bullshit or you can kiss your business goodbye.