Compare the map in TFA with this map, which I trivially Googled:
http://news.gallup.com/poll/203117/gop-maintains-edge-state-...
It's not a perfect correlation, but to my untrained eye, looking at both maps, it seems to me that red (eg, Republican) states appear to correlate closely with higher suicide states.
But please judge and compare the maps for yourself and form your own opinion.
Edit, add: one criticism is that the link I got from Google is a 2016 map.