This isn't acceptable in the least. The very fact it seems so innocuous right now is to get opinions like yours circulating to make everyone feel comfortable with it. People have got to stop thinking in the short-term when it comes to privacy.
"Oh, it's just one more data point, what can it hurt now? All you have to do is type a number in a box. You don't even have to provide any documentation to prove you aren't lying!"
Their "age verification" method is useless for accomplishing any actual age verification. So why is it still being pushed? Because the groundwork is being laid now for the actual surveillance to be implemented later.

Because today’s “AIs” are glorified T9 predictive text machines. They don’t have “self-awareness.”