Currently, the file size limit for animated GIFs is 2 MiB, the same for still pictures. As a result, users are often posting low-resolution animated GIFs, and waste quite some time trying to make them fit within 2 MiB, or simply give up on trying to include animated GIFs in their posts. I'd suggest increasing the file size limit.
An important use for animated GIFs is in bug reproducing posts on meta sites - as an example, the image in this post takes up 4.56 MiB, more than twice the limit.
The standard Imgur service specially exempts animated GIFs in its file size rules, allowing them to be 200 MB. GitHub allows animated GIFs to be up to 10 MB.
Image size limit: Why it is set to 2 MB? is a different feature request, as that post doesn't talk about animated GIFs.