It's irrelevant if rights are universal if the application of those rights is not equal.
I agree - except that they are two different arguments. People arguing for equal rights are often arguing for equal treatment.
//The fight for equality encompasses the recognition that we all SHOULD enjoy the same rights//
We do all enjoy the same rights. If we don't, tell me some of the rights that some people enjoy but others don't. Point me to some legislation which says "This group of people has these rights, but that group of people doesn't."
//..and that application of those rights should not be determined by those who want to deny them to named groups.//
Again, who is doing the denying to whom? Back to the OP, Sasha Johnson is described as a "black equal rights campaigner". So what rights is she campaigning for that she believes black people don't have, but everybody else does?