Providing arguments to xdg-desktop-menu with wildcards (not expanded by shell - either because of quoting, or missing files) expand them internally, but ignoring directory part of the argument. This results in operation on unrelated files.

The most extreme case is: xdg-desktop-menu uninstall /nonexistent/*.directory /nonexistent/*.desktop
This results in removing all files from /usr/share/desktop-directories and /usr/share/applications.
While this behavior could be expected (if documented!) for just "*.desktop" argument, certainly it isn't when there was a full path provided.

Looks like missing quoting here:

        uninstall)
            for x in $xdg_dir $kde_dir $gnome_dir ; do
                rm -f $x/$basefile  # <- here
            done

(this fragment appears twice in the script - once for directory files and once for desktop files)

Version: xdg-utils 1.1.1 (Fedora 26).

BTW I recommend running shellcheck on this (and other) script, it detects problems like this:
In /usr/bin/xdg-desktop-menu line 1411:
                rm -f $x/$basefile
                      ^-- SC2086: Double quote to prevent globbing and word splitting.
                         ^-- SC2086: Double quote to prevent globbing and word splitting.