How would you explain the close similarities between the make-up of the oxygen-carrying molecule hemoglobin in organisms as diverse as birds, horses, gorillas, and humans?

They have similar or common ancestor. The similarities inherited from the common ancestor as in the case of homologous organs. In evolutionary biology a group of organisms share a common descent if they have a common ancestor. There are many other examples like in the case of hemoglobin to prove the theory of common ancestor

Less stable  hope this