Frequently I see pre-civilization tribespeoples' lives being romanticized as a sort of ideal communist society, but to what extent was this the case? It seems that they were probably much more communal out of necessity but were there really no social hierarchies? Looking at other animal societies they appear to have basic social structures with upper and lower classes.
Then, the second half of the question, what sorts of societal shifts occurred during the transition from the neolithic to agrarian cultures and why did these shifts occur?
A nitpick, but the Neolithic is the part of the early Holocene when we see the transition to agricultural societies, so generally when we call a society "Neolithic" we mean to say they are an early agricultural society. A Paleolithic society on the other hand would best describe human societies in the Pleistocene prior to the adoption of agriculture.
As for social structure, the question is not if there is social hierarchy in these societies - there unquestionably is - but on what basis is that hierarchy decided and how much social differentiation.
Generally, distinctions in these hunter-gatherer societies are based primarily on age and sex. For instance, the wise older woman/man in the group might have some slightly higher social status, or men and women might have slightly different economic roles in the group (though not necessarily different prestige or status).
The difference between the highest and lowest ranked person in a hunter-gatherer group is also very slight. Compare a king to a peasant farmer and you see huge differences, not the least of which is their respective access to luxury or prestige goods and the sheer quantity of stuff they own. Even the most highly ranked individual in a hunter-gatherer group is not going to own that much more than the lowest ranked individual. Personal property is generally very limited in these nomadic groups in part purely because of the difficultly of transporting a lot of stuff if you are constantly on the move. Likewise, differential access to mates, food, or some other non-material benefit is going to be relatively even across a group. In these societies you don't get chiefs or kings with multiple wives or large palaces, for instance.
As for the paleolithic-neolithic transition, see my post in this thread which breaks it down more in detail.
Hi, questions on the neolithic and other prehistory are worth x-posting to our sister sub, /r/AskAnthropology