My tail folder had all kinds of junk in it. So I deleted it. Beast NPC tails were working once again after do that. But it bugged me that I deleted what seemed like needed files. So I removed FNIS Creatures using FNIS Tools. And removed the FNIS Creatures mod from NMM. And re-ran FNIS to do its thing. Then I re-installed FNIS Creatures and re-ran FNIS again. I had a new Tail folder with the right files in it, and tails were still working in my Skyrim.