I am not marking it down as a bug officially because I am not sure if it is desired behaviour (I don’t understand enough about euler).
But I find it very strange that if I adjust the z rotation in the GUI editor, the other values jump around, and I can’t figure out why (or imagine why that would be desirable).
Can anyone shed some light?
I made this but it literally took me HOURS
Are you punching in numbers, or using the gizmo handles in the viewport? If using the gizmo, do you have it on local space or world space? It seems to work a lot nicer if you type in the numbers by hand.
I don’t know the right explanation either, but I know 3D rotations are a nuisance, so I’m not really surprised. 
You can try setting them in a certain order, Z, Y, X maybe? Also, setting any(?) of them to 90-degrees might cause gimbal lock, which means both of the other axes would line up and both affect the same rotation.
Both are strange (typing and rotating via the mouse). Sorry that I am unable to explain this problem better. It is very easy to reproduce, however.
I expect the gimbal lock thing might be influencing, but I can’t believe that’s desired behaviour, it makes things so, so complicated…