This is simply untenable. Institutions of all kinds have been keeping records connected to individuals for millennia.
Try to run a school when you can’t maintain data on the students.
It's not - GDPR does that and it could even be much stricter still and we'd be fine.
You can have privacy and an institution can collect data.
HIPAA is an example of that.
All personal data should be treated with at or near HIPAA levels of security. If I give my personal information to my bank, or google, that's fine for them to look at it, but it's not ok if that information magically lands in the hands of Coca Cola for marketing.