I've always wondered where, if anywhere on the continuity someone like myself would come.
I have enjoyed TV shows, books and so on with anthro-animals (such as the Redwall series of books when I was younger) and I don't see anything objectively odd about that. I don't consider "furry" creatures to be sexually appealing, nor do I consider them to be more interesting or appealing as characters than humans, aliens or anything else you might have as a character set. I don't class myself as being part of the furry fandom, but I don't consider people who dress as Furry characters any weirder than I do LARPers or cosplayers, even though it isn't something I would do (I might LARP though, even though I never have as of this post).
People who are sexually attracted to furry characters on the other hand I find disturbing in the extreme, much like those individuals who are or claim to be attracted to inanimate objects. I think that attraction to a human being male, female, trans or whatever is something that I can understand, even if I am not attracted to that individual or that gender, but a cat? A fox? That's just...weird.
Otherkin are even weirder.
ETA: I'll clarify what I meant by disturbing.
I don't mean "You people are all sick and wrong" or even "It's harmful". As long as it's consenting adults, of course it isn't harmful, nor is it "wrong" in any objective sense, I just find it...utterly bizarre. For instance while I'm straight, I can see other men as handsome, and while I can't imagine ever wanting to actually have sex with a man, it's close enough to my own feelings and desires that I can understand it on some level, I'm just not wired that way.
Being attracted to an anthro-animal on the other hand is so far away from my own viewpoint that I can't understand it. The closer you get to being realistically animal like (e.g. cats with multiple sets of breasts or something) the further from my frame of reference it is and the more disturbing (to me) I find it. By all means knock yourself out and do what you wish as long as no one gets hurt, but I have to say I find it strange in the extreme.
As for otherkin being weirder, I take that to be someone who believes they are, or have the traits of something "other" like a dragon or faerie (I always spell it that way) because those creatures are purely human constructs. While we may have altered the actual behaviour of wolves in our minds to the point at which some people may be confused or surprised by actual wolf behaviours if all they know are the distortions made by humans, there is still a real animal that can be studied and said to possess certain characteristics.
On the other hand Vampires for instance have so many different stories written about them that it would be impossible to be a vampire.
Are you an evil risen corpse who terrorises peasants? Are you a slightly twisted and pale human who drinks the blood of virgins and lives in a castle afraid of the cross and running water? Are you a sexy cool anti-hero who just has to drink blood and hide from the sun? Maybe you're a sparkly douchenozzle who abuses his vacant "true love"? It doesn't matter what you are because they're all fictional, so there isn't a set trait or series of traits that you can feel.