Very strange. Are you sure you’re using Blender that was downloaded from blender.org and not one from a linux repository. Have seen people accidentally using the repository version a couple of times because it allows them to launch it by running “blender” command.
Even the tooltip says to use shift+click on scene layers but there are other layers you could try. It’s also possible to shift+lmb hold and drag to enable/disable multiple.
Could try these
Not sure why the shift key would be special. It might be reserved by the desktop environment/window manager but having shift+lmb there doesn’t make much sense. You’re probably able to use it with everything else in Blender, like panning with shift+middle mouse, and shift+S for snap menu. If you’re not using emulate numpad option, it should also be possible to access layers with number keys and shift+number key would add/remove visible layers.
Speculating even further, no idea how Blender user preferences -> system: selection method would affect layer selection but could try changing it from auto to either of the options. Occlusion queries is quite recent addition. Could maybe also try different window draw method. Blender UI is drawn with OpenGL so at least there is a slim chance the problem could hide there.