Mmm... Honestly, I don't believe in it. I mean, the idea of therianthropy- especially lycanthropy, is awesome enough in fantasy. Speaking of the type that you're probably referring to- with animalistic thoughts ad behaviors but no "shifting," no, I do not. I'm not against it, and if other people believe it, that's cool cool, too, because that's what they believe. I just don't care to toy with the idea. I'll keep an open mind and be accepting/good friends with the others if they do the same for me and my beliefs.
Anyways, I'm not saying I'm right or people who believe that are right, because I don't know how people would confirm it, but I always keep in mind that the brain is very powerful, especially placebos. Not just medical placebos, but just the will to believe something will make it seem true. There may be people who can truly "connect" with their therian animal, but who's to say the rest of people think they are just because they really want to believe they are, and the placebo takes effect to the point their brain tricks them? That's just me, though.
As for otherkin, that's completely different than therians. Like with therians, I'll accept and will be friends with those who claim to be so, but I don't believe in that at all. That's more of a religious thing, though, and I will admit that. I do have very good grounds and evidence for my religion's validity than I do for the existence of otherkin. Animal souls in a human body? Sure, we may have animal-like characteristics and behavior (which may stem from the fact we're closely related genetically, and humans did used to be hunters and gatherers which involves the "animal-like vicious behavior" to make a kill), but not otherkin, unless they're aliens from another planet that landed since around the time of the dinosaurs like in Doctor Who.