First, moral considerability is essentially the technical jargon in the field of morals that is used to indicate whether or not one is worthy of moral consideration. As moral people tend to grant moral considerability to all other humans, the term is primarily used in relation to other species.
As an aside, I would point out that religion or other strong ideologies sometimes cause people to treat other humans without granting other groups moral considerability. Anyone who believes it is OK to kill or enslave members of any outgroup is clearly not granting that group moral considerability.
That said, I would try to keep this post to the topic of what species other than humans should also be granted moral considerability. As I have hinted in my title by the use of the word whom for members of other species, I clearly believe, quite strongly, that many other species are worthy of such consideration. I have often surprised people by asking who that bird is, rather than what that bird is or other equivalent. I believe living beings should be referred to as who and whom rather than what. It keeps us from forgetting that they are indeed other beings, not inanimate objects.