Except anime isn't really a fandom as such, Rocoro, more like a genre of art, like it's evil twin manga, fan bases tend to be product-specific, usually those who obsess over anime are indeed otaku but otaku is the Japanese term for obsession and since the Japanese are generally very otaku about anime/manga, it becomes more pop culture than fandom, it even has historical ties.
Furry stems back to internet culture where furry was short for anything other than the ordinary animal related categories on the usenet/bbs servers and it got hijacked by what's now regarded as furries, "furry" was preferred as the spacing on the qwerty keyboard was somewhat of a nerdish like because the keys "f, u, r and y" are closer together, making it more efficient for typing. Noted in some media as furries are Shawn Keller (disney animator, seems noted for good style emphasis in films such as Oliver & Co, as because of this he was set as the visual developer in some films), Steve Gallacci (creator of the Albedo Anthropomorphics RPG), Mike Kazaleh (creator of The Adventures of Captain Jack, and illustrator of the Ren & Stimpy comic), Tracy Butler (former yerf/artspots user, who gained more notability via the Lackadaisy comic). Whoever came up with the idea of "furry fandom" as a word or any of the descriptors like "fandom of anthropomorphic animals" is unknown as in the past is was not really closely examined, no doubt they arose from media intervention (especially in relation to FurryFans.com), the true essence of the fandom was cartoon animals and the related, it just happened that cartoon animals tend to be pretty much anthropomorphic, thanks to the funny animals developments prior (funny animals was actually a core subject of furry groups and its attitudes still exist in the furry community today). Furthermore, "furries" has often been somewhat of a slang word for furry (usually small) animals, it may well have been used in far earlier works that could be considered a part of the "furry fandom" but it did become pretty much a fandom until becoming more of a community due to the self-dependence that evolved within it.'