I think they are reacting that way because he is a Grimm and his kind can see them and knows how to hurt them. Basically they are reacting to old myths and legends about grimms, expecting Nick to be some scary guy determined to hunt and kill them. But not all creatures are afraid of him, it's mostly creatures that have characteristics of animals not known to be fierce.
Monroe had no troubles jumping on him in ep1. It was a joke but he wasn't afraid of him, nor was his ex girlfriend later. Siegbarst came to his house, Lowe had no troubles confronting him and forcing him to fight, Steinadler knew Nick for what he was and offered to work with him. All these animals are fierce creatures anyway and this carries to relevant creatures as well.
Creatures that are afraid of him are ones that are not "fighters". Eisbiberwas terrified and beavers are not known as particulary fierce animals. Fuchsbaufreaked out because he was selling organs, a shady activity and one that could get him in troubles with humans. And foxes are supposed to be cunning, not fierce.