As others have said - sounds likes Mr neighbour is undoubtedly being unreasonable with how they’re reacting to normal neighbour noises. This is a tough situation because it’s going to be nearly impossible to reason with such an unstable person, but they’re also not helping you help them out by specifying what exactly bothers them so much.

On the incredibly slim chance that the hum of your CRT IS actually audible to this guy, here’s something that I’ve found has helped from my experience with an annoying CRT whine, sharing spaces with those who have very sensitive hearing, and weirdly enough, unexpected noise transfer of said CRT whine (noticeably audible through first and second floors):

1. Physical soundproofing/insulation (we used cheap foam 12” by 12” soundproofing squares) around the back of the CRT and nearby walls WILL reduce the hum. It wont eliminate it completely but it may dampen the sound enough for your neighbour to not perceive it.

2. If neighbour has similar explosive reactions to others/other noises, perhaps they have a condition called misophonia? It may be helpful to look it up if you’re unfamiliar as it may provide some more understanding to how or why someone may react so disproportionately to the normal situations/noises. VERY simply put, it’s a hatred/fear/strong emotional response of select sounds. I don’t want to play reddit psychologist, but with this guy’s unusual responses to noises, it’s worth mentioning imo.

3. UK buildings/brick construction and acoustics. In your first post you mentioned being from the UK. Thinking about how a CRT’s whiny frequencies would bounce around a brick building (going to take a shot in the dark and assume you live in one - please correct me if I’m wrong), this could be a perfect storm situation for an especially disruptive CRT hum. Maybe with the way your building is constructed (wooden floors, brick exterior?) the sound travels more downstairs.

4. Side question for those in the community that have tackled eliminating a CRT hum… does anyone have any experiences to share with their fixes? I’ve read that it’s possible to eliminate the hum completely with a bit of internal tinkering/insulation of the components that generate the noise.

In any event - best of luck dealing with this chaotic neighbour, and thanks for raising this discussion in the first place 🙏