If I had to choose a method, it would involve an authentication site - one it would have its security validated by a trusted entity and guarantee that you will be fully compensated should they be hacked. Even better if that's backed up by a large insurance policy.

You verify your identity with them. Then they verify information requested by other sites. The risk of hacking is minimized to that one company. They should collect your IP and information about your browser, operating system, and hardware. Then issue you a cookie stored on your browser.

Subsequently, when you use a website that needs to verify your age, they read your identification cookie and validate it with the identification company, asking if you are of majority age and providing the information they collected. The identification company gives a yes or no response. They do not give out any other information about you, preserving your privacy. As long as you are using the same computer on the same IP you don't have to revalidate. A hacker would need access to your computer if they wanted to impersonate you.