You're taking Tywin Lannister's words out of context and losing their meaning. Tywin said this in a sword-and-shield battle context and meant it that way. The way he acted outside of battle was more complex. For example, Tywin Lannister didn't give the Mountain any orders to kill the Taegaryaen heirs, yet the Mountain did so anyway with Tywin's tacit consent. Remember how unsure the people were in the show and book about the nature of Tywin's involvement in killing the Taegaryaens heirs? This was because Tywin Lannister planned and contrived the situation that he could could usurp the Iron throne while denying any actual responsibility for the killings to attain it. The Taegaryaens had to die but Tywin Lannister couldn't have been seen as the one to do it. So he had the Mountain do it. Tywin believed in asymmetrical warfare and "by any means necessary". He also didn't believe in your "I don't support BLM because it has fags and thugs, etc" mantra.
He was not a purist and sanctimon that you are. You say you don't want BLM to have fags or thugs or feminists because you don't agree with them. In other words, you don't want to work with people who offend your sensibilities. Your ideals are more like Robb Stark's than Tywin Lannister's. Because even though Tywin didn't agree with what the Mountain's abhorrent actions, he also believed that "even a dog has its uses". That's why Tywin allowed the Mountain to live and continue serving him. That's also why Tywin--who hated foreign sellswords and mercenaries--paid the Bloody Mummers to fight for the Lannisters. Because, again, "even a dog has its uses".
Tywin didn't always like whom he fought with; he merely hired, paid, lavished and tolerated them for the sake of his goals. And then, when the war was over and their usefulness was at an end, Tywin dealt with them. After the war was over, Tywin sent the Mountain to eliminate the same Bloody Mummers Tywin himself hired and then disavowed the same Mountain's men thereafter. I think the same way. I don't care for feminists or gays or drug dealers. I just care about black issues and spreading it. And bringing black people together helps with that goal. After my goals are partly or all achieved, I'll
It's funny how so many of you have criticism of BLM yet don't even kno what it is. Black Lives Matters isn't about integrating; it's literally just about black issues that other people, gays and wenches, sometimes coopt to further their own ends. This however does not invalidate BLM or black issues, just like someone using democratic principles to further a war campaign doesn't invalidate the spirit of democracy. Also, in terms of pro-black action, I think BLM has done a good job promoting pro-black ideas in general. An idea doesn't have to be accepted by a President to have an effect on real people and bear fruit.