I don't know if black people are shot more than white people, the thing that most people care about is that the police seems to be a lot more agressive when it comes to black people, even when unwaranted.
Lots of "SJWs" think about side effects, the reason that the conversations that they are having on twitter and reddit aren't more nuanced/allowing for "but"s etc. is that you are fighting an uphill battle with that kind of stuff on the internet. People like to pretend that the world has been taken over by PC-culture but the large majority on the internet still firmly hates Sjw's. This means that they don't really consider the internet a place for "policy"-discussion, but at best as a tool to spread the message.
(Ps, none of this may have been worded very clearly or convincingly, English isn't my first language)