You are not adequately represented on the map.
My contention would be that people in the red states are more likely to be the working poor, particularly the rural poor, and that they do not have the opportunity to purchase health insurance through their employer, for a variety of reasons. For instance, people who work at Walmart in low-skills categories are usually kept at a 32-hour-per-week employment status so that Walmart can avoid the cost of providing health insurance.
The assumption by many conservatives is that the people who don't have insurance coverage aren't willing to pay for it, or are on welfare. In fact, it isn't AVAILABLE to many Americans, and it is often extremely cost-prohibitive to those who are in the category of working poor. They earn too much to qualify for state benefits, but too little to afford insurance.
These states are also, in many cases, "right to work" states, so people in the skilled trades, who would have had insurance benefits through a union in another state, instead work in small non-union shops without access to affordable healthcare benefits.