Comment by tzs

If you do it right the only sensitive information exposed to the age gated site is that your age is above their threshold.

The party that actually has to at some point verify who you really are of course has your sensitive information, and there is no obvious way to work around that. However, there is a way to make it so that it doesn't matter.

That is by making them be a party that already has that information. Probably the simplest would be to make it be the same government agency that issues your physical identity documents like passports or drivers licenses. If we don't want it to be a government agency or we want to have competition banks would be a possibility.