This map seems correlated with socieconomic status and all the health implications that go along with that. And it looks similar again to Republican voting districts. It's Sarah Palin's "Real America", so to speak.
One thing the Democrats would do well to focus on is the fact that there's a large portion of the country that is sick, where the statistics look more like an underdeveloped country. Those of us who live in the major cities would do well to empathize with this other part of the country and their malaise, even if for our own sake of having a more sane and less partisan government.
Democrat or not, those in the "other part of the country" are the ones voting against themselves, i.e. for politicians who oppose subsidized healthcare, who oppose workplace benefits such as paternity, maternity, and sick leave, those who oppose healthy food for public school students (and public schools in general...)
Those living in major cities have empathized with those in areas that consistently vote for "smaller" government, by not voting for the same policies and politicians that are causing them harm.
The belief in smaller government and general distrust of it in some such areas (but not all) is, IMO, often because paternalistic urban policies don't effectively meet rural needs. Which is taken as proof that government can't solve their problems.
The politics of benefits in such areas are also frequently driven by a perception of affordability -- it's all very nice to have paternity, maternity, sick leave, etc., but when the perception in the community is that there are few jobs, and what jobs there are can barely afford to pay people's wages to begin with, of course it's going to be accompanied by a belief that forcing the provision of benefits is just going to destroy jobs and not help anybody.
I think it's important to take some sort of needs hierarchy into perspective - when daily living is tenuous and stressful, I think many of the benefits the "too stupid to know what's good for them other parters" don't seem to be moved by are addressing the wrong steps of their needs hierarchy, or fail to take into account the financial and environmental realities of their day-to-day lives.
Just as housing has turned out to be an important first step in combating homelessness (as opposed to medication, employment, etc.), I would not be surprised if there were different first steps needed to support people in poorer, more rural, areas than what are perceived within them as very white-collar benefits.
If the rural areas are doing poorly, it's always tempting to blame the cities, or the "urban elite", or whatever. Yet the rural areas quite often dominate state politics. If their own representatives are acting paternal, it's hard to see how it's the cities fault.
Providing help to rural areas remains quite popular across the board. There is a long history subsidizing rural agriculture, infrastructure and utilities. It's proven difficult to eliminate the poverty despite that.
State politics are often little more than a reaction to national politics crossed with support for moneyed interests like car dealerships and some grandstanding/boot-licking race-to the bottom job policies. National politics really sets the tone, context, and priorities people are aware of, especially so in an era when most reporting and commentary is national in scope and local information is often via word of mouth and social media.
I do think it's true that in many rural-dominant states you can't blame a state-level urban elite, and that's not really what I intended to suggest in my comment (though I do think in "blue" states there very much is such a dynamic, witness Jefferson, rural sheriffs flatly stating they won't enforce various state laws, etc.). Frankly, I don't think blaming an urban elite at a national level makes sense either, as I don't believe what I referred to is at all intentional.
That said, I think the examples you list of things subsidized may also be examples of things that are likewise slightly misplaced priorities in terms of the larger picture. For example, I'd imagine (though I don't specifically know that) agriculture subsidies mostly go to large enterprise farming operations and have little trickle-down effect to many every-day rural people. Likewise, subsidizing rural infrastructure seems like it may be necessary regardless of any significant benefit, though it's once again highly speculative on my part (for example, I'd guess fire-fighting services require significant external subsidies in some areas, but also don't have tremendous effect on the day-to-day life experiences of average "locals").
My previous statement is also why I think the election of Trump may be an important milestone in solving some of their problems: namely I think (hope) he may be a gateway to the realization in certain quarters that what were presumed to be their problems and solutions actually aren't, leading to a significantly reformulated and broadly unified national consensus. (Yeah, probably a pipe dream...)
There was much more involved in the election than healthcare alone. There were cultural concerns(people in big cities worry about very different things than the rest of the country), economic concerns(outsourcing and illegal immigration have brought down wages for the lower and middle classes) and even democratic concerns(the DNC suppressed Sanders from being the Democratic candidate). Those are all legitimate concerns, and on top of that you've got to consider gerrymandering and the emotional aspect of voting that isn't rational. Trump recognized a large part of the country that wasn't acknowledged by Hillary, and that boosted the Republican party as a whole.
Your post is weakened by including some popular tropes which are unsupported by the evidence.
The DNC didn't suppress Bernie – he has a great run for someone who wasn't even a member of the party but he was going against the best known name in the party who wasn't the outgoing president.
Similarly, Hillary had the same message – and a far more detailed plan to get there – but a variety of factors (Comey, propaganda, a 3 decade smear campaign, the media obsession with keeping the email story on the front page despite lack of an actual story, etc.) led more Democrats to stay home than Republicans. Both candidates had a small amount of crossover votes but by and large more registered Republicans showed up to vote.
The DNC did suppress Sanders and showed massive bias towards Clinton, the email leaks showed it. Clinton's campaign got debate questions early. They got preferential treatment in the media. Then when Debbie Wasserman Schultz, the DNC chair at the time, was kicked out because the collusion became public knowledge, the Clinton campaign _immediately_ hired her. If there wasn't massive collusion, then there was at very least an image problem, which Clinton did nothing to help by hiring the very person forced to resign.
Also, the message sent by the two were not identical at all. Sure, if you tallied them all up and compared them by existence they would be very similar, but the difference was in the focus. Sanders' campaign focused on socioeconomic inequality which would have resonated more in rural America, while Clinton's campaign focused more on social issues, which matters more in the urban centers where the economy is less of an issue.
> the ones voting ... for politicians who oppose subsidized healthcare
It's more complex than that, because those same voters are pressuring their elected representatives to retain healthcare subsidies and similar benefits.
One thing the Democrats would do well to focus on is the fact that there's a large portion of the country that is sick, where the statistics look more like an underdeveloped country. Those of us who live in the major cities would do well to empathize with this other part of the country and their malaise, even if for our own sake of having a more sane and less partisan government.