- Animated avatars were allowed but disabled years ago. Because forum members saw animated avatars are annoying and the core admin (theymos) had the same opinion. He stepped in and code to detect all animated images for avatars and reject such images when people try to upload for their avatars. Only grandfather members still have animated avatars today. But if they take their avatars off, and upload same images again, forum will reject it.
- Animated signatures would be more annoying than avatars so no chance to see allowance for it.
If you are curious, this one is for you.