When it is the right call
Some forum software, chat platforms, ad networks and older email systems maintain hard-coded format allowlists containing GIF and nothing newer. When that is the wall you have hit, GIF is the answer.
The colour cost
GIF allows 256 colours per frame. A full-colour photograph squeezed into that palette shows visible banding and dithering, particularly in skies and skin tones. Graphics, memes and flat illustrations survive well; photographs generally do not.
The transparency cost
GIF transparency is 1-bit — each pixel is fully opaque or fully invisible. WebP's soft anti-aliased alpha edges become hard and jagged, which is very visible on a logo placed over a coloured background.
The size cost
Converting an animated WebP to GIF typically grows the file three to five times. GIF's compression is decades behind, and there is no setting that closes that gap.
Better alternatives where allowed
If the destination accepts anything more modern, animated WebP or a short MP4 will look better and weigh far less. Use GIF only under protest.