Short of genetic modification, we are always going to live in a world where your opportunities depend on the characteristics you were born with. We can smooth it out somewhat, but not remove it completely.

Look at discrimination against unattractive people for one - it is actually more pronounced (although less overtly visible) than discrimination by race, but gets significantly less media coverage. There are also many other axes - height, intelligence, character - most of which are heavily influenced by genetics; we simply consider it acceptable to discriminate based on these attributes.