Keyboard settings changing partially/not at all in Ubuntu MATE
Solution 1:
Many thanks to @pomsky for pushing me to change settings and see the pattern.
The reason was the fcitx utility which lived its own life and was overriding MATE keyboard widget.
Solution:
$ sudo apt remove fcitx
$ killall fcitx -9
$ killall fcitx-qimpanel -9
Solution 2:
I had the same problem, but the solution to remove fcitx
did not work for me because it wasn't actually installed. Instead, it appeared that the keyboard preferences in Control Center got overwritten by iBus preferences (also in Control Center).
Creating two layouts in iBus preferences along with the keyboard preferences helped to solve the problem.