Bullshit. Google is telling them to remove content if they want to comply with Google's advertising T&C, otherwise the ads won't run and they won't make money. That's not censorship; if you're running an ad-supported site, you have to run ad-friendly content. If Google is paying you to run their ads, you're their piper, and you play the tunes they call.
That is censorship. Sometimes large businesses remove their advertising from a paper publication because they disagree with the reporting. When that happens, the whole industry rightfully calls it censorship and abuse.
> If Google is paying you to run their ads, you're their piper, and you play the tunes they call.
You just described censorship in crystal clear terms.
No, that is not censorship. You calling it that does not make it so.
Consider the alternative: Either morally or legally, Google and/or their advertisers have to run ads on sites that they disagree with, thereby supporting them both financially and reputationally. Where, in that scenario, is their free speech?
You're free to say anything you want. I'm free to not endorse it or support it. So are Google and their advertisers.
(You might make a case for actual censorship if Google refused to index such pages.)
It is censorship, even though they have the right to do it and even if they can have justified reasons for doing it.
During war, letters home from soldiers and even generals are read by a censor and censored, so that sensitive information cannot get to the enemy. That is legal, that is agreeable, that is still censorship.
In this case, Google even specifies what articles need to be removed for continued advertising, so it is crystal clear censorship.
The definition most of us use for censorship is "I prevent you from saying something." What Google is doing is "I decline to help you make money from saying something." That is not at all the same thing.
Prevention is one way to censor. Prohibition is another. Suppression is a third. In this case it is suppression by economic means. There are degrees of everything, including censorship. Google withdrawing ads because they don't want to be associated with a publication is a different thing than Google sending dictates on exactly what is allowed to be said for continued business.
Is Google breaking any laws? Probably not. Are they practicing censorship? Yes, they are.