Your question is a bit like asking if ice cream sales are linked to murder rates. It’s true that there is a link, but only because there are other things going on that affect both. There is no causation between the two. In other words, being conservative doesn’t automatically mean you do more crimes, and doing crimes doesn’t make you more conservative. There is a lingering variable here, which is poverty and income inequality. The parts of the US with the most poverty are linked with high crime rates because people do crimes when they are desperate. And people living in poverty are often poorly educated and can be susceptible to the appeal of conservative dogma, which is often about laying blame for poor economic outcomes, even if it’s mislaid.

My answer is only with regards to the US and I am not speaking to other places. In many countries there is an actual left-wing party which offers an appealing alternative for the working class. In the US, your options are the Republicans, who acknowledge you are poor and tell you it’s because of things like government overreach and minorities, or the Democrats, who will just pretend you don’t exist if you are poor unless you are also a minority.

Rural areas have a higher violent crime rate per capita than urban areas, but that’s not quite the same thing.