It can be achieved with a zero-knowledge proof - there are many schemes, but in essence, they all allow you to prove something (e.g. your birthdate, validated by a government agency), without revealing who you are. You can prove to a third party "the government authenticated that I was born on 1970-01-01" without exposing who "I" is.

Some worthwhile reading on the topic if you're interested:

https://en.wikipedia.org/wiki/Zero-knowledge_proof#Zero-Know...

https://en.wikipedia.org/wiki/Blind_signature

It should even possible to construct a protocol where you can prove that you're over 18 without revealing your birthdate.

Zero-Knowledge Range Proofs: https://eprint.iacr.org/2024/430

"Zero-knowledge range proofs (ZKRPs) allow a prover to convince a verifier that a secret value lies in a given interval."

The anonymity is that the government doesn't know who is asking for the verification, not that the the government doesn't know whose majority it should attest.