Dangerous to poke around inside when plugged in, but quite safe unplugged (unlike say an old TV).
a CRT monitor is typically (I would not gamble on it - again!) not safe when unplugged
I just saw the words "unplugged" and remembered the word vacuum tube - then massive emotions from my past came rushing through
the capacitors in CRTs could store a charge for a long time. i've seen people that assumed the caps were discharged find out the hard way when they shorted the leads with a tool. the noise alone is enough to make one need clean shorts. the only good thing is that they discharge quickly, but they give you "both barrels" worth to borrow a phrase.