In our system, "Narnian pronouns" refers to a pronoun preference shared by the non-humans of West Voidelia/Blue's Supercluster and the Moon Aura Marsh (in Bryan's Supercluster).
West Voidelians and Moon Aura Marsh (who are Narnian alterhumans) prefer people use Narnian pronouns for them, which means they use it/its and a "binary" pronoun (i.e. he/him or she/her), with or without they/them and neopronouns, and they prefer humans to use "it/its" for them and for non-humans to use "he/him" or "she/her", with no preference for who uses they/them or neopronouns.
Only non-human headmates who use it/its and a binary pronoun use Narnian pronouns. For example, Clutch is a West Voidelian non-human, but sie uses they/them, it/its, and some specific neopronouns. Since it does not use she/her or he/him, they do not care what pronouns people use for them regardless of their species relative to hirs.
Non-human headmates in West Voidelia usually distinguish their species by setting a member of it to their icon, or using a source image that makes their species clear. Moon Aura Marsh is all non-humans by default.
This also only applies to headmates from West Voidelia (which is the most connected to fiction and The Chronicles of Narnia) or the Moon Aura Marsh (which is comprised of Narnian alterhumans but is an East Voidelian region).