There are blind, privacy-preserving ways that this can be done. A third party verifies a government ID and issues an age-verification token. The token is passed to the porn site, which has a way to verify the token without talking to the entity that issued the token.

That way the porn site doesn't know who you are (it just knows "this person is old enough to access this content"), and the age verification entity doesn't know what you used the token to access.

Of course, this scheme is more complicated than building an age verification system that involves uploading a government ID (or asking a third party directly to verify someone's age), so ultimately no one gets any privacy or anonymity.