Possibly. The social dysfunction of rural America is a really big story that I think needs more attention. It's not just the suicide rates, either. There's a relative lack of academic accomplish, low productivity, low life expectancy, high obesity, etc.
To be clear, I'm not arguing the individuals who are killing themselves are conservative. I'm arguing that the societies controlled by conservatives produce a lot of people who kill themselves. That's a clear difference. Alaska has long been dominated by Republicans, who set policies that impact liberal and conservative residents alike.
First, no, suicides are the MUCH bigger problem. The US has about 15.3 suicides per 100k, versus 5.3 per 100k for murders.
Second, I'd be happy to discuss murder rates. Murder is disproportionately a red-state problem. The highest murder rates are in the South, which as a region has a rate of 6.4. The region with the lowest murder rate is the Northeast, at 3.5. The worst states, in order, are LA, MO, NV, MD, AR, AK, AL, MS, IL, SC, and TN, in order (TN and SC are tied, so I listed them both. Of those, eight went for Trump and only three to Clinton. At the other end of the spectrum, the best states are NH, ND, ME, RI, ID, MN, VT, NE, UT, OR, and MA (OR and MA are tied). That's seven for Clinton, four for Trump.
So, what do you think it is about conservative-dominated states that makes them so violent?