It's definitely not a materialist position, so it can't be a Marxist one.
"One party states have similar power relations and thus end up similar whatever their ostensible ideology is" is a materialist hypothesis.
Whatever the socio-economic differences between the 1910s Russian Empire and 1930s Germany, a significant similarity between fascism and Leninist/Maoist type communism is that the masses have little political voice and thus can exert only the crudest leverage on government policy (threat of passive or violent resistance). This is a similarity also shared by other forms of bad government such as feudalism. This is a material similarity.
Eh, I definitely agree with that it's highly mythicalized, but the Shire parts of The Fellowship make it quite clear that class differences exist in the Shire, that there more reputable families and less reputable ones, that there are rich people (like Bilbo and Frodo) and that there are even people in relative poverty (but of course, since it's the Shire, they don't actually go hungry). Sure, the social inequalities are somewhat mitigated by Hobbit customs, but they are definitely part and parcel of the entire social makeup. I think that all is sort of ancapish, just not the stereotypical image of ancaps we have where everything is corporate; but it pretty much is rich people being rich without any pesky state interference and being looked up as the reputable people in society, while that all is presented as an ideal setting.
Are the rich hobbits actually capitalists, or are they more like rich feudal land-owners or influential big men?
I haven't read LOTR, but I'm guessing that "idealized rural utopia as imagined by a conservative British guy in the middle twentieth century who was modelling it on what he saw as the best of traditional English society" would look more... anarcho-feudalist, if that makes sense? Like, you'd have moderate economic inequality because there'd be some families who have more and better land and/or were more diligent and clever in improving it, and these rich families would have prestige and powerful offices to go with their wealth, but these rich families would also have
noblesse oblige and share their wealth with their less fortunate brethren (and their prestige and powerful offices would be tied to this
noblesse oblige), and the whole system would be held together by a thick network of a mix of egalitarian and hierarchical mutually beneficial relationships with mutual obligations, and the whole system would work to moderate socio-economic inequality and create a sort of "every family owns its own at least moderately successful farm" utopia. Such a society might have some proto-capitalist features (e.g. a significant
petite bourgeoisie of the "family that is prosperous from owning their own water mill or shop or brewery, the employees are mostly or entirely family members" sort), but its basic structure would be feudal; land ownership as the primary form of wealth, most people are farmers, most wealth is held by families instead of by individuals, small or nonexistent proletariat, little in the way of a labor market, certainly nothing like a stock market, etc.. This fits with the idea a paleoconservative utopia; that sort of paleoconservative perspective would frown on features of a truly capitalist society like a large landless laborer class and a large and well-developed labor market, as those truly capitalist institutions would tend to promote social atomization, destabilize traditional community and family relationships, increase socio-economic inequality, and increase class tensions.