Weird, I don't feel nearly as touchy about some ones and zeros on a computer as I do my physical body's safety, without which I would not exist.
What matters is if the thing they're doing to test your security is similar to what criminals would do to breach your security.
In the case of a physical location, that bar is low. It's things like seeing if your garage door is open, or your car doors are locked, etc.
In the case of computer resources, that bar is high. Probing your database for permissions holes is absolutely something that a normal "cyber criminal" would do. It's the equivalent of a carjacker looking to see if your doors are unlocked.
So an "online neighbor" alerting you that your database is unprotected doesn't feel weird at all. It's not the equivalent of that weird laser pointer thing you talked about, it's the equivalent of looking to see if your car doors are unlocked while you're away on vacation.
As someone else mentioned this would be more akin to a security officer of some sort waking me up and letting me know I left my front door open. I'd sure as hell be shaken but they were doing their job and I'd be thankful for that.
If i leave that filing cabinet in the middle of Times Square in Manhattan (which has an insane amount of foot traffic every day), then yes, I would expect plenty of people to give it a little wiggle to check if it’s locked. And I would be rightfully given a lot of questionable looks for complaining that passerbys stop to check it out or give it a wiggle.
Having your service on the internet is not the same as having a filing a cabinet in your house. I think that the Times Square analogy is even underplaying it, given that on the internet, your audience is many many magnitudes larger and more remote/anonymous.
On the other hand, if I had a private VLAN (that wasn’t exposed to the internet) on my home network, then I would be definitely annoyed if my houseguests would try and pentest it without asking.