To begin with, you cannot download gif images at some sites like X or pixiv. If you want to get the image you have to use external tools.
I checked sites and sources page and tried YouTube-DL, cobalt.tools and Jdownloader2. For YouTube-DL I tried "youtube-dl -F <URL>" but it stated that X's status page is not a valid url. Copy gif address doesn't work either because it only directs you to the status page. For Jdownloader2 it only catches an invalid package from the status page link. Whether they just can't get the gif image or it's not how I use them properly. The remaining cobalt.tools can get the image, but the quality isn't satisfying. Take the post below as an example:
post #5593062
This gif image has resolution of 1920x1920, by contrast the image obtained from cobalt only has 1280x1280.
There are 2 other tools mentioned in the wiki page, but PixivUtil2 is for pixiv only and Idem's Sourcing Suite is said to be "outdated and broken for X". For the latter I don't even know how to use it because the example image is unavailable.
I believe there is a way to get the best quality, but I have no idea how to do that.