Japanese Folklore in Brand New Animal

General
Michiru Kagemori and Nazuna Hiwatashi’s transformative properties and designs allude to the folklore surrounding tanuki and kitsune, who both tend to have shape-shifting properties and other supernatural talents. In particular, the kitsune is described as being able to transform from a fox into a beautiful woman in order to trick or befuddle humans. Nazuna could be described as doing the opposite of this- beginning as a human and being unwittingly transformed into a fox beastman and using this ability to obscure her human origins.

Episode 5
During the baseball game against the flamingo team, one of the flamingos mocks Michiru, suggesting she sails away to Kachi Kachi Yama on a mud boat. This jab references the folktale of the same name, in which a villainous tanuki (referred to as a badger in the original translation,) ends up competing against a rabbit in a race in a mud boat and sinks.

Episode 6
While describing the concept of transformation in the attic, a tanuki statue is shown on screen, referencing the folktales of tanuki being able to disguise itself by transforming into humans, animals, and inanimate objects.

Other Folklore
The species of Sato, Tanaka, and Yamada may be a reference to the fable of The Deer Without a Heart, which also involves a trio consisting of a deer, a fox, and a lion. Additionally, both Yamada and the deer from the fable end up losing a body part that another character views them as not deserving of: in the case of Yamada, his antlers, and in the case of the deer from the fable, his heart (being from a time period in which the heart was viewed as containing knowledge and wisdom, similar to how the brain is viewed in modern times.)

Alan Sylvasta's godlike form of a three-headed canine bears resemblance to the three-headed Cerberus of the underworld from Greek mythology.