Why not use the more natural example? “What if a television network decided the same thing? We will watch your publicly broadcast television show and if you say something we don’t like we will cancel your show.” It’s a lot closer to what’s actually happening in this case, right? And it doesn’t needlessly mix in the hot-button topic of privacy violations.
The parallel is phone companies in the past did listen in to people’s conversation, but this was recognised as an abuse of a monopoly power. Regulations were introduced to stop this sort of activity.
What we should be discussing is how to regulate natural monopolies like YouTube, not if they should be able to just do whatever they like. Like all regulation there will need to be a balance, but society has a vested interest in ensuring natural monopolies are not abusing their power.
Even if YouTube is not abusing its power, the fact it can is a concern.
Some services are so large and entrenched that they have become natural monopolies that need to be regulated. We place restrictions on what natural monopolies can do because of the effects on society as a whole.
The question that needs to be debated is if YouTube has reached the status of a natural monopoly or not. I think it probably has, but I am open to evidence on the other side.