Earlier quoted context omitted.
In practice though with the GDPR, sites either just 403 everyone in the EU to avoid complying, or just shower you in javascript cookie notifications, making your browsing experience more bloated, slow and insecure.
The GDPR is not a law that only regulates the internet. The GDPR applies to all processing of all personal data regardless of whether that's pieces of paper in a filing cabinet or an entirely online social network.
Insurance? Private doctor? Youth services? Family (or any other) court? Pharmacy (in most of Europe)? Police (even in the most trivial of cases, and without judicial approval, and of course without verification or recourse)
Worse than that: the exception goes further than merely keeping data as well. Insurance company wants to change/add to your medical record? Immediately? Doctor? Court? Police? All can change your medical file, both adding and deleting (sometimes limited to what they added themselves). YOU want to change it? Not possible!
Weird since insurance company access to your data, and "the right to be forgotten" was one of the main selling points of this legislation, but since insurance companies are semi-government in almost all of Europe these days, a lot of them fall into the blanket exception.
And of course, you yourself ... cannot access this data. You cannot see it (sorry "you can, unless there's a reason not to let you see it", wanna bet there's always a reason?). For particular parts (espectially names, for example which doctor put something there about you are kept secret from you). Thankfully these institutions hate eachother, so there is some protection left because if anyone wants this data, they have to file requests in 5 different places. But there is no more legal protection against this happening.
It is now far easier, in the Netherlands, to get a serious crime stricken off your judicial record than, say, getting a doctor or pharmacist's claim that you falsely came in for a heart problem out of your medical file, say to threaten or attack them for painkillers, or even just getting the name of which doctor put that there (and of course such misleading information can kill you if you ever really do have a heart problem, and god help you if you need pain killers or ...)
GPDR protects you from Amazon offering you gift ideas for your kids' birthday if you object to that. You want a mental health stay 40 years ago to not be used in a family court case against you? THAT it makes MUCH easier. Faking such a thing and using it in a court case against you, that, too, it makes a lot easier.