This is meant to touch on some common biases I see crop up a lot on tumblr, new otherkin, etc. Note that 'bias' doesn't necessarily mean a heavily slanted extreme opinion, but often just an illogical opinion that an argument should not be based on if it wishes to stand firm. Bias is building the house on sand, so to speak.
Definitions taken from Wikipedia, but these are quite common definitions you should find in any psychology textbook or scientific research manual. My additional comments are added in [bracketed italics], and any sections I find particularly relevant are underlined.
Confirmation bias - the tendency to search for or interpret information in a way that confirms one's preconceptions. In addition, individuals may discredit information that does not support their views. [I feel like this is a major problem for the otherkin community.]
Self-serving bias - The tendency to claim more responsibility for successes than failures. It may also manifest itself as a tendency for people to evaluate ambiguous information in a way beneficial to their interests.
Anchoring - The tendency to rely too heavily, or "anchor", on one trait or piece of information when making decisions (usually the first piece of information that we acquire on that subject).
Anthropomorphism - The tendency to characterize animals, objects, and abstract concepts as possessing human-like traits, emotions, and intentions. [One of the most common biases I see in the community, for obvious reasons. Do animals experience emotion? Yes, but we cannot call it by human terms or claim that animal personalities are similar to our own, because we do not have a window into their minds that tells us exactly what they are thinking.]
Bandwagon effect - The tendency to do (or believe) things because many other people do (or believe) the same.
Curse of knowledge - When better-informed people find it extremely difficult to think about problems from the perspective of lesser-informed people. [I'm including this because I do see a lot of older folks being very aggressive in their correction of misinformation. I understand that having been in the community for such a long time, it is aggravating to see history repeat itself and definitions become more and more twisted plus humans are just plain stubborn all the time, but I don't know, maybe because I'm newer I still have an idealist idea of a gentle approach? ALSO please don't take this to mean I'm talking about anyone specifically, just that this is something I do see in general.]
Focusing effect - The tendency to place too much importance on one aspect of an event. [Dreams are a good example. I may be a dragon in one part of a dream, but the same dream may also contain me riding a rainbow through the castle.]
Stereotyping - Expecting a member of a group to have certain characteristics without having actual information about that individual. [Anti-kin obviously do this a lot, but it can also apply to stereotyping certain creatures based on assumed traits, such as "all angels are sweet and good" or "all demons are violent and angry".]
Subjective validation - Perception that something is true if a subject's belief demands it to be true. Also assigns perceived connections between coincidences.