It would not be obvious
to me that the narrating neighbor is doing anything unacceptable. Your appeal to obviousness (bandwagon fallacy) leaves out any meaningful ethical argument as to
why such behavior should be socially unacceptable.
One neighbor has a right to record, memorialize, or journalize anything they may observe. The other neighbor has a right to privacy, sometimes.
But that does not include those times when they are out and about in public. If you don't want neighbors tattling on your activities, be somewhere where they can't see you without trespassing. There is a case to be made for a right to pseudo-anonymity in public, to not be gratuitously identified by strangers, but this does not apply to your hypothetical.
Please take a moment to think past obviousness, and consider the non-obvious implications of establishing a right to privacy based on invisible-to-the-human-eye private property lines and the potentially obfuscated ownership or unpublished tenancy rights in those properties.
The only question that needs to be answered is whether the owner of the camera has the right to be where the camera is while it is recording. Opening it up beyond that, to what the camera might be able to capture from there, is a whole new can of worms. That introduces the potential for censorship based on the content of the recordings, a possibility far more unacceptable (to me) than having a relentlessly snitchy, nosy, tattling neighbor.
There is definitely an argument to be made against police being able to use all those shared video feeds without getting explicit permission from a judge, but I believe the doorbell-camera owner has an absolute right to record anything it can see, 24-7, and publish all of it, or none of it, to whomever they choose to share it with, or no one at all, to include turning it over to police. It is not meaningfully different from the nosy old fart that watches everyone in the neighborhood from their front window, and then gossips about what everyone is doing to their friends, who are doing exactly the same thing on their own streets. They can tattle to the cops whenever they like. We have always needed to draw the curtains to keep Peeping Tom and Bertha Busybody at bay. Preventing them from looking anywhere off their own property is not an ethical option. We can restrict the police from acting on those tips without independently verifiable evidence, because the cops are nominally public servants.
And that's where the focus needs to lie. Restrict the cops from even looking at any of those shared feeds without some record of reasonable suspicion.