> New York Times that criticizes the New York Times,

This has happened.

> the government to decide what is allowed to be banned and what isn't,

This is a civil lawsuit where people are trying to a) prove they were harmed and b) be compensated for that harm. The government is just the referee.

> Meta is removing these ads, because pretty much any advertising platform would do the same about ads that criticized it.

Which was not very smart because the next step will be a court order requiring them to put a banner on ever page with a link to sign up to join the lawsuit - for free.

Online stores don't remove 1-star reviews of their products from their store. Do they ?

This may sound reasonable but isn't at all how newspapers are run. You can absolutely buy an ad in the New York Times criticizing the New York Times. Within reason of course, as you said the are private entities allowed to take on any customers they want, but in general newspapers hold journalistic integrity as an ideal and will allow most things as long as they aren't defamatory, unethical or downright illegal.

The ad sellers and the journalists are normally separate and will not interfer much with one another's work. It also helps that they never say no to money. I don't know about the New York Times specifically but similar things have happened many times in other newspapers, and there is such a thing as a paid editorial. Those are usually clearly marked as such, but it's basically the same thing.

(However, there may be other reasons why you might want to go with a competitor instead, and not pay the newspaper you hate $100k.)