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