To what extent must you feel animalistic to be a therian?

People who claim to be therians have their own idea of where the line is drawn, yeah, a line unique to them. As long as you consider your animal to be nonhuman, I believe therianthropy starts with the faintest sense of its presence. ("Their" presence in case of a polytherian or -kin, just to complete)

What others have touched upon here, namely that human beings aren't that far apart from animals, is what I would consider very important to hold into account as well. It's no secret that humans and animals have common ancestors, so it's not that hard to believe that their traits both can overlap and therefore can be mistaken for those of solely a nonhuman easily. Happily even, in case you're eager to explore the community like many of us do. Guess it depends largely on what the individual thinks of their traits. Do they consider them to be atypical for human beings? Are the traits so tied into their personality that it means it impacts their functioning, reasoning, thinking under daily circumstances highly? And how do we interpret the verb "to impact"?

Well, according to my reasoning, there is an impact from the moment you believe some of your actions stem from an atypical, alternate, nonhuman influence. This influence doesn't have to be tied to a certain and constant trigger either. Sometimes, it depends on how we're feeling (sad, emotional, sleepy, angry,...) that allows us to shift or act more animal-like but it doesn't have to be the case each time that trigger frequents. Feeling other than human is not always something concrete like a shift, a vocalization or a dream of sorts. It's also, like I've been meaning to say too, about feeling distinctly off among humans. Abstract yes, but... Feeling off really needs to be present. Not all the time, but it appears to be a commonality in many.

Now, a few psychiatric conditions may cause disassociation from human beings or the feeling of being alienated among them. Heck, even neurodiversities may contribute to that feeling also, even if those aren't exactly therianthropy, the notion that one doesn't belong is as equally real as it is with a therian, methinks.

In conclusion, things like these are highly individual. People who consider themselves wolves, yet aren't according to our principles or understanding, may as well be considering there are an equal set of wolves as there are individuals. So, what we should do is listen to each other and not dismiss others' beliefs because of the differences there may be.