I’m not a criminologist, but I do know a little bit about it.
First, crime statistics can be notoriously unreliable. It’s hard to get a perfectly accurate depiction of what’s going on in the streets, so to speak, because of jurisdictional differences in regard to the definitions of certain crimes, emphasis in enforcement, etc.
For instance, the rise in crime in the 80s could be related to an enormous increase in the population band that generally commits crimes (males, 18-25, maybe 30). As the Boomers began to hit that age bracket, there were more people in the band that commits crimes, and so, more criminals.
Or it might be that police were enforcing crimes more routinely than they did previously. Or it might be a change in the way we used statistics. It could be a number of things, and there are academics who spend their entire lives trying to put the pieces together.
As far as cultural arguments go (secularization, &c.), I’m not sure there is much of causal relationship. Crime rates have decreased significantly from the 80s. Aside from a cities (like Chicago), violent crime rates continue to decrease. But if I’m not mistaken, “secularization” has increased even more rapidly. If secularization WERE the cause of increased crime rates, we’d expect to see MORE crimes committed now than even in the 80s. But we don’t see that. So I’m not sure it makes sense to theorize that non-church-going leads to a higher crime rate.
In other words, no one can really be 100% sure what is going on. I think any person who studies this stuff carefully can only come to the conclusion that the answer to, “Why does crime increase or decrease at any given time?” is simply, “I don’t know.”
ETA: I’m not sure about divorce rates, though.