If you point out that my front door is unlocked, and I decide to keep it unlocked forever (i.e. refuse to fix it), then it doesn't mean that it somehow becomes ethical to enter my house and take my stuff. It might be stupid on my part to keep it unlocked, but a thief is still ethically a thief even if I carelessly kept it unlocked forever. My "door" might as well be a line in sand or a sign "don't enter" on a pathway - not a security measure at all, just an indication where the boundary is, but still unethical to cross it. Much more so would be sending a note "lock your door, send me money or I'll take or damage your stuff", as in the original example.
Threatening to harm someone unless they do what you say is immoral even if you don't harm them; it's not ethically acceptable to threaten others.
If you had classified information behind your open door, you could be sued if anyone stole it (or worse, depending on the level of classification). Sometimes, one is legally required to take appropriate steps not to unwillingly disclose information. I believe users' personal information should fall under this category. (I believe it does in some cases.)
If your leaving the door open leaves not only you, but others, vulnerable, the discoverer of the broken lock may very well have a moral obligation to protect those innocent people, by whatever means appropriate.
What is appropriate depends on the situation. I expect in most cases, just telling you the door is open may be enough. But if you are being particularly obnoxious, threats may be the only way. In some extreme cases, burning the house down to avoid the disclosure of the sensitive information that would harm countless innocents may be the best course of action.
The legal system even have analogous situations, where a judge can order the orderly destruction of some unsafe building. The only (yet crucial) difference is, judges aren't vigilantes. But this is fixable: one could have the law allow the vigilante to send a cease & desist letter saying "fix your door or I'll have a judge burn your house down".
Threatening to harm someone unless they do what you say is immoral even if you don't harm them; it's not ethically acceptable to threaten others.