From an outsider's perspective, an owner of a server can ban anyone they want for any reason. It's their server. As some of you say, just find another server to play on.
This practice of some admins using anydesk to remote into a machine to check for cheating software is just plain dangerous. Its potentially worse than an invasion of privacy. If someone has remote access to your machine, even while you are watching, there is nothing stopping them from installing whatever they want. One could install something with an innocent name like 'Minecraft cheat checker' and the child watching thinks that its all normal but that software could have additional payloads such as keyloggers, viruses, webcam spy software and so on.
I am sure that the vast majority of admins are acting perfectly innocently when they use anydesk. However, it normalises what is an exceedingly dangerous practice. Indeed my son insisted, 'This is normal. Its what happens on Minecraft'. From a child safety point of view, I was horrified!
The machine my son was using has been wiped and we've had a chat about IT security and what the dangers are.