Because the replicants still weren't human. Sure, they LOOKED like humans.
Basically, it tugs at the heartstrings. Looks right, feels right, but still is NOT the same thing.
So I think that while every person might indeed be tempted to legislate along these lines, it's only really the left who would.
Perhaps I'm naive. Maybe the appearance is all that matters. I mean, I don't think dogs have souls, but it is and should still be against the law to mistreat them. Perhaps the same kind of principal would apply?
That is far and away enough to qualify for civil rights.