‘Personal data’ means any information relating to an identified or identifiable natural person (‘data subject’);

They store his personal data without his permission.

also

Information that is inaccurately attributed to a specific individual, be it factually incorrect or information that in reality is related to another individual, is still considered personal data as it relates to that specific individual. If data are inaccurate to the point that no individual can be identified, then the information is not personal data.

Storing it badly, does not make them excempt.

Maybe he has a insta profile with the name of his kids in his bio

Irrelevant. The data being public does not make it up for grabs.