"Anonymous" identification for the internet age - a question for the crypto community

I was just reading a reddit dicussion about age verification online and got to thinking about BCH/ETH and other smart contract platforms and tying in with Monero/Zcash style ZKPs (all of which, it seems, will be coming to a cashtoken near you ... "soon" I hope).

Would it be possible to create a digital token for a person which could then be used as an ID everywhere BUT, in a provably anonymous way. i.e. the website or 3rd party service verifying the specific details about you would obtain no information - instead they would only obtain a ZKP response to the specific question they asked - for example, "is the user >18yo?"

Such a token could be issued at birth and could be expanded to include much more than just a person's age (e.g. genetic data, health, financial, lifestyle...). But ALL the data would be provably securely encrypted and inaccessible even to the service provider asking questions about the data. Inaccessible even to the token issuer (presumably the govt).