What do you think of Maine, Vermont, and New Hampshire often matching western states to an extent in being libertarian, small government, rural small towns? Maine and Vermont were the only states to oppose FDR in one year after all.
It's a good question, and highly relevant to the current electoral season. Trump is YUGE in New England, but much less so out West. (See the map in this NYT article, and some discussion in the comments of this post.) That right there says there can't be too much in common between the political sensibilities of New England and Texas / Utah / California.
First, there are almost no small rural towns out West -- the original settlement proceeded very fast because it was driven by get-rich-quick schemers pouring in searching for virgin niches to exploit. Lots of small towns implies slower population growth.
Most people west of the Mississippi either live in large cities or their surrounding suburbs and exurbs. The exception is the northern Plains, but those rural residents don't really live in small towns so much as family farms in wide-open town-free expanses. Sure, folks who live in Missoula have easy access to unmolested nature -- but they don't actually live out there. They live in a city or a suburb.
So the person out West who prefers lower population density doesn't actually want to be part of a tightly knit small town, but to be a rugged individualist (at most accompanied by a nuclear family). That means either an urban or suburban mountain LARP-er, or someone who lives in a remote area -- unattached to a broader network of other people and institutions.
The low-pop-density person back East longs for the cozy intimacy of an interconnected group of families and peers.
Libertarians would probably refer to this difference as "communitarian" vs. "individualist" libertarianism, but it seems like a false similarity since the core of libertarianism is laissez-faire. Small-gov communitarianism vs. small-gov individualism, is more like it (small-gov being a modifier, not the essence or substance, which are radically opposite).
Perhaps it's more useful to ask what the two groups want in place of a large state that intervenes and regulates their local area. Communitarians want a rich network of civic institutions and organizations that are bottom-up, where members regulate one another. These are the "third way" solutions that Elinor Ostrom surveyed in the undeveloped economies -- neither leaving things up to an unregulated market, nor having top-down state regulation or control. Their closest analog in the developed world would be those whose disappearance is chronicled by Robert Putnam in Bowling Alone -- labor unions, fraternal organizations, the PTA, and so on.
The individualists want more of a culture of honor solution. It's not as though there aren't any livestock herders back East -- but they aren't known for rustling one another's cattle, or getting into armed stand-offs with the government over grazing rights. The lawlessness and disdain for society is familiar from other cultures of honor around the Mediterranean and Middle East, particularly among nomadic pastoralists rather than settled agriculturalists.
There is another important difference -- over religion. New England communitarians are not very religious, spiritual, or anything like that. West of the Mississippi, the individualists may or may not be religious, but it's a decent possibility as opposed to non-existent. And their religion is feverishly apocalyptic -- understandable if their worldview lacks any man-made regulating forces, whether bottom-up or top-down, meaning that chaos and annihilation are always just around the corner. If there are no natural regulating forces, that can only mean that supernatural forces determine our outcomes. Divine intervention takes the place of man-made regulations.
In this way, the libertarians out West are similar to the Islamic fanatics in the anarchic Arabian culture of honor. White converts to Islam and ISIS sure seem more common out West than back East.
It also accounts for the out-West mania for the Old Testament, Israel, and "Judeo-Christian" values. The God of the Old Testament must be properly treated because he holds our fates in his hands, and we want to stay on his good side. That comes from the days when the Jews were just another bunch of Semitic pastoralist hillbillies, living in a mostly lawless environment. Likewise the folks out on the American frontier approach religion from the angle of propitiating the only regulating force in the world, there being no such forces down here on Earth.
Back East, communitarians are more non-religious. But to the extent that they are religious, it's more Christian than quasi-Judaic. The New Testament is more focused on man's relation to one's fellow man, usually from the point-of-view of reforming one's own inner character and actions. Divine intervention plays a minor role, and therefore so does propitiation (praying for God to intervene, offering him a sacrifice, etc.).
In a way the Christian movement was taking the first steps toward a bottom-up, man-made system of regulating our behavior so that we don't blow our society up, although the man-made system is treated as having a divine origin in the man-god Jesus Christ. This began when the Jews had settled down more into towns with more permanent civic groups and governments, compared to their more lawless days as nomadic herders.
Hence the Eastern communitarian's preference for mainline Protestant or Catholic churches, and feeling alien at a more evangelical happening.
Easterners also come from the historical core of the country, and feel more of a responsibility for tradition and stewardship, whereas the Westerners who hail from the rootless frontier shrug that off in favor of creative destruction, what they imagine is the outcome of laissez-faire. This is reflected in their church preferences, with mainline and Catholic churches having deeper roots and more codified rituals than whatever the trend du jour happens to be among evangelical churches.
That shows up in their feelings about government. The communitarians want there to be some kind of institution that preserves historic places, and that regulates the altering or destruction of existing natural and built environments. For individualists, nothing should get in the way of good ol' creative destruction and re-development, if that's what the individuals involved want (past and future generations do not get a say in the individualist / libertarian world).
There's more to say, but you get the idea. There really isn't much of a libertarian strain back East, certainly not in New England. Call them communitarians, civic cultists, descendants of de Tocqueville, or whatever you want, but they aren't rugged individualists or de-regulators. Although desiring a small government, they still want a rich system of social regulations in place, only locally and from the bottom-up, and connecting a tightly knit social network rather than isolated households run by the paranoid bunker mindset.