I had to choose "other", because my position on the matter is full of
ifs and
excepts. For the most part, I'm kind of against "animal people" because they're just kinda dumb and bland (as are elves and dwarves, really). But, at the same time, I've got to confess a weakness for lizardfolk. I just kinda dig the whole reptile people angle, as long as they're not going to be presented as anthropomorphic iguanas or something. They've gotta be their own thing, no more lizards than humans are monkeys.
Also, there is nothing that makes a new arrival to the House Rules forum stand out as a somebody to be scorned faster than a "Check out my cat-people race! PEACH" thread*.
But when it really comes down to it, I don't violently dislike "furry" characters so much as furry
players. I'm aware that there are sane furries out there, but their ratio to the
completely intolerable furries is not a favorable one. My primary objection to playable animal people would simply be the danger of attracting more irredeemable nutjobs to D&D.
Ha. I know your campaign has cultists who turn themselves into gnolls.
* "They have +2 to Dex and Cha, claws that do 1d6 damage, and are always Chaotic Good. They are somewhat flighty and always curious. The females of their race rarely wear clothing."