Why should that information be protected in the first place? It's not much different than a phone book. Your full name, address, phone number, etc are all linked to your identity. Once someone has one, it becomes nearly impossible to stop them from getting the others.
The problem with doxxing is that it usually comes with a threat of violence from ideological opponents. I think what many people should be fighting for is the right to anonymity. For your identity to never be revealed in the first place. Free speech can't truly be expressed if having the "wrong" opinion leads to some wingnut smashing your head with a bike lock.
Maybe a right to anonymity with the efficiency losses you get there is worth it? Tough issue.
And why should a celebrities and public officials have different standards? Either it's fair to judge someone by a certain past action or it isn't.
And yes, the issue isn't that it's new, it (like many internet social issues) is scale. A few bad actors locally to now thousands world-wide.
Curious if HN has any ideas how to approach that issue?