I managed to get Mate in 16.04 working by using system dafault value for XDG_DATA_DIRS.
I set in .profile
export GSETTINGS_SCHEMA_DIR=/usr/share/mate:/usr/share/mate:/usr/local/share/:/usr/share/:/var/lib/snapd/desktop export XDG_DATA_DIRS=/usr/share/mate:/usr/share/mate:/usr/local/share/:/usr/share/:/var/lib/snapd/desktop