It’s a good job that these monitors aren’t valve based devices.
In a lot of old valve TV's many used PD500 triodes as (I think) shunt stabilizers for the EHT. Due to the EHT that they work with, these valves emit quite a lot of X-Rays when in operation, and, in the same way as you have noticed on your monitor, have warning labels.
Unfortunately repair engineers had to work in close proximity to these devices whilst the TV's were powered up and with the metal shielding protection removed in order to be able to fix the TV.
Btw, PD500's have been used to generate X-Rays for photographic experiments just like those of Amiga hardware here on Amiga.org . There’s a website about it somewhere.
Another point - If you ever decide to dismantle your monitor and give it a really good clean, amongst other things don’t clean the black gungy stuff off of the back of the CRT that looks like baked on muck. That’s actually "aquadag" and is used to prevent the X-Rays from escaping from the tube (My experience shows that solvents, such as methylated spirits, tend to remove it quite well...)
Hodgkinson.