The reason why full moon cats bite may be because they are learning how to use their teeth for protection and socialization. Kittens begin to interact and learn how to use their teeth to protect themselves around the full moon.
In the process, they may bite fingers, arms or other objects, so it is best to give them some alternatives before they bite. Give them something to bite, so you can prevent them from biting you. Additionally, cats may bite because they feel fearful or threatened. If cats feel uncomfortable in crowds or ignored, they may bite to express their displeasure. So, if your cat bites frequently, it's a good idea to seek help from a veterinarian or an animal behavior expert to determine the cause of the biting and find a way to resolve the problem.