Learn English – term for a child born after the death of its sibling

The closest I can find to what you're describing is "news-induced" or "media-induced" anxiety. A quick search does not indicate widespread adoption of this as a catchphrase, but it seems like a sensible fit.

"Stranger danger", as you cite, is something that arose out of a particular kind of bad news that was prevalent at the time. I am not aware of any similar catchphrases around computer hackers, spying, terrorism, etc.

In mental terms, someone excessively worried about such things might be "hypervigilant" or suffering from "anxiety disorder". Or just plain "paranoid".

There are some generic idioms about "jumping at every shadow" or thinking that "danger lurks around every corner", but I think those are probably too broad for what you're looking for.

In psychology, it is called doorway effect or location updating effect.

Researchers already know that walking from one space to another makes people more likely to forget tasks when compared to others who don’t make such a transition. Called “location-updating effect” the phenomenon also causes people transitioning between rooms (even virtual ones) to take more time while attempting to recall items from memory.

news.discovery.com

It happens both in virtual and real environments; and it is explained that leaving a place and entering a new one is served as an event boundary in the mind and memory refreshes itself for the new information.

This “doorway effect” appears to be quite general. It doesn't seem to matter, for instance, whether the virtual environments are displayed on a 66” flat screen or a 17” CRT. In one study, Radvansky and his colleagues tested the doorway effect in real rooms in their lab. Participants traversed a real-world environment, carrying physical objects and setting them down on actual tables. The objects were carried in shoeboxes to keep participants from peeking during the quizzes, but otherwise the procedure was more or less the same as in virtual reality. Sure enough, the doorway effect revealed itself: Memory was worse after passing through a doorway than after walking the same distance within a single room.

scientificamerican.com