There are plenty of ways to do it such that the verifier doesn't know why they are verifying and the relying party doesn't know who was verified.
As far as I understand, the ISO 18013-5 mobile drivers license standard (which appear to be being implemented across a bunch of US states, including California[0]) seems to allow for each fact that appears on your license to be individually signed so that you could store your ID on your phone, and then when prompted, provide only your birthday or only an "over 18" marker that's signed by the state.
The service provider could then not keep any records except to mark your user as a verified adult so in the future you can just login.
