Right, there’s a wide variety of data requirements and age verification these days — I think under GDPR ideally the birthdate would be used to verify compliance with age requirements, and then no longer be stored.
In the US the requirement to verify age can sometimes be a higher priority, because regulations like COPPA restrict the processing of children’s data.
Either way, if you’re capturing this information it should be treated as personal information, you should only store what’s necessary (this is where a lot of the variance is), and it should be protected appropriately.
Anyone that’s unsure should consult a lawyer in their area!