Considering that the poor don't pay taxes, that doesn't make a lot of sense.
The other way to think of it is that the feds have their tentacles into everything. Sure, there are all the military facilities. That's one thing. But there is highway funding, education, and a whole laundry list of things that the feds throw money at. The sparsely populated areas that tend to vote red are going to draw a disproportionate share of some of that. I mean, how much $ in highway funds does North or South Dakota receive relative to one of the more densely populated northeastern states? Or Montana? Or Wyoming?
No doubt, I think that if the red states were to form their own separate country, places like Mississippi and Alabama will be fucked regardless, but that has little to do with GOP policy.