I can reproduce this XIM problem on a system which was upgraded to 16.04, but not on a fresh Ubuntu 16.04. However: If I create and switch to a new user, the problem is not present. In other words: Some leftovers from previous version(s) in the home directory of my main user prevent the XIM input method from working properly.
Resetting the gtk-im-module gsettings key, as mentioned by Piotr, doesn't help for me. Neither does removing of the whole gsettings database ~/.config/dconf/user
For the record: On Ubuntu and most flavors, switching to some other input method can be done from the Language Support GUI. Doing so changes the ~/.xinputrc file instead of removing it.
I can reproduce this XIM problem on a system which was upgraded to 16.04, but not on a fresh Ubuntu 16.04. However: If I create and switch to a new user, the problem is not present. In other words: Some leftovers from previous version(s) in the home directory of my main user prevent the XIM input method from working properly.
Resetting the gtk-im-module gsettings key, as mentioned by Piotr, doesn't help for me. Neither does removing of the whole gsettings database ~/.config/ dconf/user
For the record: On Ubuntu and most flavors, switching to some other input method can be done from the Language Support GUI. Doing so changes the ~/.xinputrc file instead of removing it.