How can I change the Ctrl+Shift+U shortcut (and others) to work as expected in Texmaker instead of being caught by Ubuntu 18.04?

As per this Stack Exchange Answer You need to run:

im-config -n none

The screen with the Unity interface looks like this afterwards:

settings language.png

Notice the last field has changed from iBus to none. Unfortunately I don't have a Gnome Desktop screenshot for you.

A newer method (if im-config is not installed on your system) is with gsettings:

$ gsettings set org.gnome.settings-daemon.plugins.keyboard active false