While there is a harmless side, the "ick" side has been taking over -- people who dress up in fur costumes to have sex. They have become the freaks of all freaks in geeky fandom and are considered freakier than even the anime fans and LARPers. The kinky stuff has become enough of the "face" of Furry fandom that the show "ER" made fun of it in an episode --a Furry shows up in the ER and so does a famous hand puppet from a children's show (think "Lambchop"). The "punchline" has the Furry stealing the hand puppet and, well, pleasuring himself with it. If anime worries you (anime also has a very harmless side), I'd be just as worried about Furry fandom, expecially if it involves making contacts online or attending a fan get together. There are some very creepy people and some very creepy art out there.
Thanks for the additional information. We're careful about the websites she visits, but I'll have her dad check the computer, again. And get-togethers of any kind are definitely off-limits!