While care is required, designing a system that only proves that someone is over a specific age is possible without leaking much additional information.

For example a request for age verification can be generated and signed by the porn site. All it needs is a unique ID and the signature. It should expire quickly and can only be used once.

The person identifying themself can send this request to a certifying party (the government in the EU where we trust governments, or I guess some terrible for profit company in the USA because they privatize everyday). The certifying party can sign the request, since they know how old the person is.

The person then returns this verification to the porn site.

In this scenario the porn site never learns anything about the user other than that they are above a given age. The certifying party only knows that the person has gotten an age verification, but not why or where.

There is still possible collusion between the porn site and the verifying party, but in that case the system is not really needed at all. Also metadata tracking is possible (like when a person gets a request and has network traffic to a porn site), but can be mitigated if a user is concerned.