> Who defines the terms "Nazis" and "terrorists"
On their platform, YouTube does.
I apologize if I'm accidentally misunderstanding what your expectations are regarding decisions in society, but if you're asking for society to eliminate judgement calls, this is an incredibly unrealistic ask and you will almost certainly forever be frustrated.
Everyday humans make judgement calls, and they seem to be reasonable far more often than they are unreasonable. If YouTube's userbase feels YouTube has become unreasonable, they move on to another platform. Whether you realize it or not, in a society based on private property, where we allow individuals to have control over things they own, what may seem like arbitrary judgement calls are necessarily made thousands of times per day. Everything from the local bartender who must decide when someone has too much to drink to the person choosing which stocks to buy, to the interviewer deciding who the best candidate is for a job. Judgement calls are constantly made. In a society which worships private property and places an incredibly high value on individual choice, Asking "who decides X, Y, and Z?" will always end with "The person who owns the thing or is placed in the trusted role for that decision." You interact with this trust over and over and over again throughout your day.
Now if you want to question whether or not a society should worship private property to the level with which we do, this is an entirely different question. But in our current iteration, where we trust individuals to make decisions without seeking permission from every member of society, the owners of something or the people they hire decide what is or is not do with their personal assets.
It likely isn't possible to run a society where no one is ever making judgement calls. Again, if I misunderstood the implications of your question, I apologize.