There is a loose correlation across states that are typically red and states that are typically blue: https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_violent_crime_rate
I can speak about the mountains of North Carolina and the surrounding areas. My stomping grounds were between two tiny towns, Andrews and Murphy. Look it up on a map if you would like. It's probably similar but also extremely different to other places. This is my experience alone but it may give context to any other comments.
Let's talk about politics first.
From my perspective, and where I grew up, poorer and fairly isolated populations tend to be a little less educated and extremely religious. They are vulnerable to manipulation by religion and politics because both are heavily connected. It's a cycle that is taught and passed down through families, to be honest.
Politics that focus on blaming others for their misfortunes seems to work really well. It's super easy to blame issues on people and cultures they have never met since all they know is what they have been told.
Education plays a role, but not a huge one. Teachers of the local schools likely grew up in the same area. Heavily biased discussions of religion and politics in schools is fairly normal as well. (One of my science teachers constantly reminded us that evolution was evil, but he had to at least mention it by law.)
Crime is an interesting thing. Drug and alcohol abuse may be rampant in smaller communities. It's just that there is nothing better to do than get fucked up and breed. With drug addiction comes crime. It's worse because jobs are already limited and many people are at or below poverty to begin with. At least in my old town, murders we uncommon but cases of domestic abuse, robbery and other crimes were astronomical. When crystal meth showed up on the scene in the late 90's, it was like adding gasoline to a fire that was nearly out of control to start with. A good number of my highschool classmates either didn't survive or are probably still in jail.
Edit: I was a fairly extreme alcoholic for a number of years and started drinking very early in my life. I quit that shit though and I absolutely blame it on how I grew up.
There is a commonality between most of the people as most of them don't want to leave where they grew up. Sure, many of them do go out in the world for a bit, but most of them just go right back home.
People who leave that life tend to be more educated, maybe have a little more money and will generally completely reject anything from their past, especially religion and politics. (Oh. That last bit was easy to describe because its me and a very tiny circle of people I grew up with. We are spread across the country though, so we really don't talk much anymore.)
It's weird though. Through all the bullshit, I still kinda miss the place. There is nothing in the world quite like being miles away from society and in the middle of the woods. Where I grew up was an extremely beautiful place, society excluded.
So. I intended that to be a neutral analysis, but it probably never could've been. Hopefully, it gave you a partial answer to your question.
Edit 2: Sorry about the wall-o-text. I could probably write a book about this stuff since I hardly scratched the surface of your question. There are many layers to this, from an insiders view anyway.
