No one truly believes in total equality. No one believes a nazi is equal to a talmid chacham. What you are referring to is just equality. That a man should be equal to a woman, or a kohen should be equal to a levi or someone who is a natural talmid chacham should be equal to someone who tries his best but never attained stature. The simple answer is in olam hazeh there is not just equality, but in olam haba Hashem will work everything out.
Justice is a Jewish value. The fact that Hashem is just and treats everyone justly (i.e. based or ones bechira alone, and not based on what sex they are, who there father is, or what genetic advantages they were given in olam hazeh).