I don't think you'll have to give all your data to random websites. You'll be issued a single use token with a yes/no flag saying if you're over 18.
That's it. It's so, so much less data than what people are mindlessly giving to social networksthese days. Contacts, birthdays, private conversations, credit card numbers, personal photos, minute-by-minute IP and geolocation. Those are all things that social networks take for granted and governments don't (and will not) have access to.
People are making a giant fuss about "them gov'nmint" but completely ignore all the data social networks already have. And you can simply not use them if you don't want to give "all your data to government". I know I won't.