I'm running ubuntu 16.04 LTS, and have used the "Keyboard" application to set my "Compose" key, but every time I do the key retains its old function. I've tried this with "Caps Lock", "Right Ctrl", and "Menu", and have logged out and back in between making the change with no effect.
The change is saved in the "Keyboard" application the next time I log in, and I can also check it in
$ /usr/bin/gsettings get org.gnome.desktop.input-sources xkb-options ['compose:menu']
I have to specify the path for
gsettings because when I don't I get the following message:
$ gsettings get org.gnome.desktop.input-sources xkb-options GLib-GIO-Message: Using the 'memory' GSettings backend. Your settings will not be saved or shared with other applications. @as 
I think this has something to do with the
gsettings in my Anaconda installation in light of https://askubuntu.com/a/943739/457920.
The keyboard layout I am using is "English (international AltGr dead keys)", and the "AltGr" key in that layout works fine for me. The "Compose" key still fails to work when I switch to the more basic "English (US)" keyboard layout.
Has anyone else experienced this problem or know of places to look for the source? I've found the question Compose key not working on Ubuntu 16.04, but the behavior there doesn't match my situation (the question poster had "Compose" working in some, but not all, applications, whereas my "Compose" key doesn't work in any application I've tried, mostly Firefox and Terminal).
Edit: One additional point about my setup that may be relevant is that I run both Unity and xmonad as my window managers. xmonad uses the "Super" key for special things, so I suppose there's a possibility that it is messing with the keyboard layout in a conflicting way. The problems I describe with the "Compose" key are present both when using Unity and when using xmonad.
Edit 2: Upon request, I tried setting the "Compose" key in a guest session, and everything worked fine there, so that seems to be a clue.