Beyond demonetization, YouTube did categorically ban videos demonstrating how to install and/or fabricate an autosear. In practice, this also extends to purely educational videos explaining how an autosear works.
Which ones? All of them? Who asked them? What about gun companies, they do not want any ads?
In fact, monetization creates a perverse incentive to prioritize financial gain over informing the public.
This is 100% analogous to what Google are doing with respect to demonetising youtube videos, and troubling for exactly the same reasons.
If tech companies start deciding that certain gun content (to use the example in the parent) shouldn't be allowed, that will of course have an effect on the general population's opinion about guns and gun rights given their market control of online video. To me it's fairly obvious that this channel of media can be used to control what people think is "normal" or "allowed".
It did not carry weight of the law, you COULD still go to a Jewish shop and buy something, but the message was that the society disapproves, the state disapproves and you are a dirty being for doing so.
The result was severing of an important daily interaction between Jews and non-Jews. Once such casual contacts were severed, it was easier to convince the society that all Jews were evil, without the people having doubts like "but ironmonger Katz is such a nice person!" They did not know ironmonger Katz anymore, only a caricature of his people.
As rayiner said, the government can't get around the First Amendment's guarantee of freedom of speech by only allowing the seller of a work to do so for free. Demonetization of certain topics on a blanket basis means that content creators have less incentive to make videos that they would have made otherwise, harming their potential audience.
For example, it wouldn’t get around the first amendment for the government to say “we’re not banning this book, you just can’t charge money for it.” (I understand that Google as a private actor is permitted to engage in censorship while the government is not. My point is that demonetization is clearly censorship because of the government did it it would be illegal.)