The same icons and gtk themes will also work with mate. The window manager
theme (mostly the window title bar) is what is different, as far as I know.
Regarding menu entries you can modify the corresponding .desktop files to be
shown or hidden in specific desktop environments using 'OnlyShowIn,
NotShowIn' keys.
https://specifications.freedesktop.org/desktop-entry-spec/latest/ar01s05.html
For example, including 'OnlyShowIn=XFCE;' in the .desktop file that
application will be only displayed in xfce.
