There is a line between furry and bestiality, it depends on how many animal traits the fursona has. Some like the kemonomimi it's basically just a human with some animal traits like ears and sometimes paws but that's all. Others are outright animal species with humanoid traits. Either way, some people might consider bestiality even the little animal-ear ones, be it in real life or in-universe.
I'm currently writing a story where my protagonist is saved, and later becomes friends with a humanoid dinosaur-like beast that they call "dragon", and it becomes a problem when people in-universe start to think she might have a thing with him. While some people just joke about it, others feel disgusted and reproach her, and some even threaten her with violence, even when she herself finds him repulsive.