I never heard of goats eating a tail off a horse before. From the first post, I assumed the whole tail was removed. However, a later post indicated only partial tail removal. I could imagine a goat eating the HAIR off the tail but NOT including the tail bone. The goat would have to be awfully close without being able to be kicked. Which could happen in close stalls.
Could the horse have some kind of disease or infection? An infection could have caused the tail rot. That could have been a possibility if the whole tail isn't gone and more and more is disapearing.
As for the cult thing. Yes and no on that issue. Yes there are "cults" out there that may do this kind of thing. However, cults don't exist soo much in "secret" that something isn't already "amiss" in the surrounding area. People can only belong to "cults" by knowing about them. So someone would know someone who was in a cult nearby. The police would also have reports.
Horse tails do have a significant meaning or use in some cultures. Kind of like a "lucky Rabbit's" foot. I am not sure what having a horse's tail meaning is. You may look that up on the internet somewhere. I believe it may have "Native American" history. However, an Arabian's horse's tail is pretty. If someone took it, it may just be for "show".
I hope the horse is okay and getting treatment. Is it possible to tie something like a rope with a ball on the end to lengthen whatever is left of the tail for temp use? The ball or object tied at the end may help it stay out of the way but still be able to swing it like normal. The rope on it's own would just go "Crazy". Good luck!!!