It's a good thing you answered your own question with putting "black" in front of civil rights.
Check what the definition of "civil rights" means. By definition yes, fighting for marriage equality, income equality, etc are all placed under civil rights "TECHNICALLY".
The thing is because of semantics and everything, the black movement in the 60s was referred to civil rights.
I'm not B'sing or anything btw. Just been straight up. Honestly i think some people would agree it would have been best if we referred to it as something specifically as for Blacks.
So we would not keep having this "education is the civil rights of our generation", "gay rights is the civil rights of our generation "Dream act is the civil rights of our generation,etc type of comments.
Everyone has their own unique fight for rights and should be set apart.
They really should have called it the Black Power Movement