Abortions? Try getting one in Texas. State sanctioned racism? No, now it's from the GOP to make it harder for them to vote. Blacks have same rights? Maybe, on paper, but they also still fight racism in many areas. Homosexuals can marry? Yeah, in some places and only after fighting for it and they still don't have equal rights across the US and still deal with homophobia.
So no, they don't need to shut fuck up. They need to keep yelling, protesting, putting it in the face of dogmatic ignorant, racist, sexist, conservative morons like you. It's actually people like you that need to STFU.