@Alyana, I haven’t tried this in Ubuntu Mate yet because I am still using 16.04 in it and the drag-and-drop works, but I have been playing with Arch Linux and the GTK3 version of the Mate desktop, which has the same problem rearranging the Favorites on the Advanced Menu. My workaround was to add all the Favorites, then edit the file .config/mate-menu/applications.list in Pluma and rearrange the Favorites the way I wanted them, then reboot without using the Advanced Menu, and my changes were retained.
It’s not a fix, but it’s a workaround if you want the Favorites arranged the way you like them until a fix is released. If that file path isn’t the same in Ubuntu Mate, there is probably one similar.