I think about this and how it changes in a specific area with stranger danger in the 1980s. The world for a lot of people was not considerably more dangerous that in previous decades (at least a lot of people who got super afraid of strangers). But the threat of strangers to your kids felt so much more real, in part fueled by rabid consumption of cable TV. It's ironic because the chances of a stranger doing something terrible to your kid are far lower than you or a relative/trusted friend doing something terrible to them, but that's another story.
I grew up during the kidnapping panic of the 70s and 80s and, I've looked back on it and realized what caused it and how fundamentally silly the whole thing was, allow me to explain:
When you think of kidnapping, you probably think of a stranger. This is true for most people which explains the fact that when the authorities saw a massive increase in kidnappings, they started the "Stranger Danger" campaign in an effort to teach kids not to get into vans with creepy looking guys who offered them candy. That makes sense if you are working under the assumption that the kidnappings are by strange, creepy looking guys offering candy.
The irony is that the increase in kidnappings was NOT due to a sudden inexplicable increase in creepy guys offering candy to kids. It was something else entirely:
In 1960 the US Divorce rate was rough 2 per 100,000 people. It started climbing in the mid 1960's and roughly tripled by the late 1970s/early 1980s.
It is hard to tell exactly how much, but it is likely that nearly all of the observed increase in kidnappings was due to custody battles. In 1960 divorce was quite rare. Modern, "no fault" divorce didn't come along in most states until much later so back then one party had to allege a wrong committed by the other then prove it. Under the modern "no fault" regime that went away. If a couple can't stand each other then they can just get a divorce.
When divorce skyrocketed, custody battles ensued. Nearly all of the increase in kidnappings was caused by the non-custodial parent (usually dad) picking up the kid without the custodial parent's (usually mom's) permission.