Why Are Red States Economic Failures?

The big issue here is cause and effect. 

Are Red States less affluent because the implement bad policies, or is this a consequence mostly of having people with deep rooted cultures that are ill adapted to current conditions that lead to weak economies and poor policies?

It is certainly true that even elite policy actors frequently are mistaken about why good policies work and why bad policies don't, even when they are right about what policies are good and bad. This often leads to bad solution to real problems.

Razib Khan has noted that lack of support for public libraries in the South that is alive and well today, and outright large rates of illiteracy and poor support for education, dates back to the 1850s at least.

From Theodore Parker’s The great battle between slavery and freedom (1856):

In 1850…Arkansas had 97,402 white persons under twenty, and only 11,050 attending school; while of 210,831 whites of that age in Michigan, 112,175 were at school or college. Last year, Michigan had 132,234 scholars in her public common schools. In 1850, Arkansas contained 64,787 whites over twenty, – but 16,935 of these were unable to read and white; while, out of 184,240 of that age in Michigan, only 8,281 were thus ignorant, – of these, 3009 were foreigns; while, of the 16,935 illiterate persons of Arkansas, only 37 were born out of that State. The Slave State had only 47,852 persons over twenty who could read a word; while the free State had 175,959. Michigan had 107,943 volumes in “libraries other than private,” and Arkansas 420 volumes….

A cultural anti-intellectualism is absolutely a barrier to good policy, especially when the gut instincts of a culture run counter to what makes sense as good policy today, even if it was adaptive in the circumstances in which it arose.

On the other hand, policy differences can lead to immense differences over multi-decade time scales, even in places that once shared a common culture.

South Korea thrived, while North Korea has sunk into squalid totalitarianism. Germany's division into East and West left the West much better off, despite the fact that historically, the economic divide in Germany was between Northern Protestant German and Southern Catholic Germany. The Middle East looked like it had a bright future in the 1970s, and then regressed into religious fundamentalism that also damped the quality of life more generally.

Also, politics, because it is basically a fight for control over monopoly control over everything, can give rise to situations where the incentives of the key actors lock them into a suboptimal state that is very hard to upset from within.

The worst countries in the world, like North Korea, are not necessarily the least stable politically. And, as scores of independence movements and revolutions that were initially successful in the 19th and 20th centuries have taught us, seemingly positive political and economic reforms are often short lived, and degenerate into one party states, dictatorships, or even, as in  the case of North Korea, de facto monarchies.