No apart from maybe primitivsts and anarcho-primitivsts these groups do NOT want to go back to living as hunter gatherers.
And in general viewing "primitive" societies as an ideal to strive for is pretty novel. For the most part when people looked at it they saw a lack of everything and usually reacted with disgust. Like the term "primitive" usually has a very negative connotation and was regularly used to justify colonialism and exploitation by the more "civilized" societies.
Hobbes et al apparently even went so far to describe the "state of nature" (so his idea of primitive societies) as a war man against man and that only the absolute monarchy and the submission to a leviathan has provided them with peace and order.
There had been counter ideas of a "noble savage" and as civilization as corrupting element, but either way people were more or less guessing what live before history must have been like and their encounter with "humans living in the wild" was usually not characterized by a genuine inquiry of a different but equally valuable way of life, but usually as an opportunity to exploit and subjugate and to see oneself as superior to others.
Recently talks about that might become more relevant given that our economy has reached scales where it's destructive rather than constructive, exploitation, toxicity and waste and the climate change that is going to effect us negatively for a long time and can get worse the more we push it. So models of sustainable existence might take examples from what we previously insulted as primitive.
That being said at the time when these ideologies emerged primitive societies were far away (both physically and in terms of being pre-historic with no accurate idea of how things actually worked back then) and especially Marx et al were not a fan of that. On the contrary Marx even praised capitalism for being way more efficient than it's predecessors and saw it as a necessary stage of development. Oversimplified he looked at society as one interconnected system and basically argued that this system needs labor to reproduce it's state of existence. If you spend 24 hours a day of work and regeneration to produce food for the next day than you're running in circles, if you produce more than that you're free to spend part of the next day doing something else.
So the collective labor and the development of more capable means of production was seen as a necessity for the surplus economy and thus a necessity for human liberation. No longer a slave to nature but a master of ones own life.
So the criticism of the economic system is that the energy that is expended in pursuit of the advancement of that system is often disproportionate to the outcome. So lots of people make it run and run faster with their labor, but few people extract ever more benefits from it. So despite the technical ability to improve the conditions and to liberate people, they get further enslaved to pay for the privilege of the few.
So the idea is how could one reorganize society so that one doesn't loose all these benefits of collective production, but achieve a society of equals where freedom is universal and not a privilege.
You can idealize a hunter-gatherer society to something like that, but usually a society of scarcity develops different socio-economic characteristics than one without it. So not sure you can compare them.
On the other hand right wing reactionary movements usually aim for a particular period in the rather recent time. Like if you go beyond folklore and cosplay nonsense the middle ages weren't all that great, cities being permeated with the smell of feces, no sewage, no internet, not even newspapers or books in quantity and availability. An aristocracy that feasted while a peasantry that struggled from harvest to harvest, wars, rape, pillages. So the further you go back in time, usually the less appealing it's going to be, so you usually aim for that sweet spot of nostalgia of idk 20-50 years ago (or just a few years further back so something that your parents marveled about but which you've never seen in person and thus believe to be larger than life and of a perfection that you can't imagine). Something that people can relate to. Something that you might have admired as a kid before your adult self peeked behind the curtain and was less than impressed.
That might be nonetheless mythological and often enough conservatives and reactionaries aim to preserve or restore something that never was to begin with but which they just imagined as such, but they nonetheless have a concrete idea of something that they think was like that in the rather recent past.
So it might happen that ones communism or anarcho-communism are achieved somewhere people end up being conservative when they defend it against changes or reactionary when they try to get it back after having failed.
Though given that ideally communism and anarchism aren't really concrete systems but rather modes of operation, similar to how a democracy isn't prescribing what should be done or how it should be done, but merely that whatever is done should have it's legitimization by the people rather than by the whim of a monarch, it's probably different to defend that vs defending the privileged rule of a particular party or person.
Like it's easier to prevent "the wrong person" to be in power, than to prevent anybody from being in power. It's a constant struggle between empowering the individual slave to be an equal participant without having them enslave others with their power. That is quite a different beast over just exercising power and fending off adversaries.