What is an Otherkin (non-spiritual)?
e: Or (spiritual) for that matter.
This first of all hinges quite a bit on what definition of religion one happens to use, but...
In a nutshell, Otherkin are adherents to a non-hierarchical, non-dogmatic, highly individualistic, and tolerant religion concerning the beliefs of those who do not identify as a member of their own species. Many believe in having the soul of a different animal or fictional creature, have faith in reincarnation, claim to receive insights through visions, meditation, and other New Age practices, and tend to feel they are trapped in a foreign or otherwise incorrect body. There seems to be significant overlap between the views of Otherkin and of people in the "furry" community.
In my case, supernatural explanations and beliefs are rejected as a default but I regard an other-than-human shape as sacred and more symbolically representative of me than the body I exist with as a flesh-and-blood human being. I do not feel like I am in the right body, would eagerly accept the animal shape I consider sacred - if ever somehow offered to me, and I still at times experience dreams from the vantage point of a body that is not human in shape and capabilities. Being agnostic, I think there is at least a chance supernatural phenomena and beings could be real, and am interested in the (albeit extremely remote) chance of an afterlife where I could continue on in the "correct" body.
The number of peer-reviewed studies out there dealing with these sorts of views could be counted on one hand as of the last time I checked, but there is very little doubt in my mind that there is a naturalistic explanation for why people like me are the way they are.