There are various ways in which age verification can be done without sacrificing privacy. Sadly, that requires standardised digital ID combined with several privacy preserving technologies that I’ve only seen used experimentally (I think Yivi comes closest, but its protocol involves sending identifiers between their servers and the consuming service, and requires services to be registered rather than arbitrarily accessible).
In its core, these protocols use digitally signed attributes (could be “SSN” or “birthday”, but more practically this could also just be “is over 18”). With this system, you can simply transmit the token that says “I’m an adult”, the website verifies this, and you’re done. To prevent abuse through infinite reuse, these apps need to be verified occasionally, and the secrets must not be stored somewhere they can be copied from easily, but phones have solved that problem ages ago.
Unfortunately, I don’t think governments who support these restrictions will also invest into these technologies. Perhaps efforts such as eIDAS will allow for some kind of non-profit to create and generate these tokens based on your standard digital government ID, but as of now, there’s nothing.
Any technology can be bypassed by kids (just steal dad’s porn pass!), so there’s a limit to how effective age gates are. On the other hand, anything that requires stealing stealing devices protected with a PIN will be sufficient in most cases.