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So if we follow this interpretation of 'treat equal cases equally' then blacks would have a prima facie right to be treated the same as whites. Gays would have a prima facie right to be treated the same as straights. And so on.

That sounds good to me. But maybe it only sounds good because we have chosen cases that we think ought to be treated equally. On this interpretation, ANY group of people would have a prima facie right to be treated like the group of all other people. Murderers would have a prima facie right to be treated the same as non-murderers. 

When you look at it that way, it doesn't seem as plausible.