We could see it the same way we see banks. Banks are private entities but tightly regulated and their activity is overseen by their operating country.
Applying a given set of restrictions and requiremnts to services used by more than 50% of the population for instance could be a thing.
In the US I know people would call bloody murder, but other countries could do with sensible rules of that kind.
It was strictly private censorship at the time - Australia didn't pass legislation to censor it yet. But it was coordinated across the entire industry - basically all ISPs used the same list, so the customers had no choice.
It was also completely non-transparent - the blacklist was secret, and they wouldn't even confirm or deny whether any given website doesn't open because it's on that blacklist.
Yet, since the government was not (officially) involved in any of that, there was no review and no appeal...
That argument seems a slippery slope towards reverse privitization. Who determines what companies are allowed to censor? Who censors the censors? Companies censor content because they are primarily afraid of liability (legal, political, cultural). There are other video sites out there. Just because youtube is popular doesn't prevent people from hosting content on other platforms.