The problem is that they're not a society, they're a tribe. Any policies of theirs are internal to their clan. They aren't a socialist society.
I'm not sure I understand the distinction you're making between 'tribe' and 'society' - tribes are certainly societies. Do you mean that they're not really a coherent society, but merely an identity group within a society?
In any case, I think an argument can be made that they're some variety of reactionary non-Marxian socialist - Utopian, Quasi-Primitivist, Feudal. Socialism as a term and concept existed before Marx, but was poorly defined. Marx invents 'scientific' socialism (from which practically all modern socialist thought derives), but of course he acknowledged and defined those movements that preceded him as follows: Socialists are those which recognize the damage wrought by capitalism on social relations, and seek by some programme to repair that damage and restore social relations. Among these were feudal socialism, petty bourgeoise socialism, utopian socialism, etc. But Marx considered most of the early articulations of socialism to be either reactionary or misguided because they were unscientific.
Now, if one wanted to argue that the Brotherhood was socialist in a pre-marxian sense, they would say: what is a greater damage to social relations wrought by capitalism than an atomic war, and the parafascist excesses of late capitalism? Indeed, this is precisely what the Brotherhood was founded upon, preventing another holocaust and the horrors of late America. They accomplish this by limiting the extent to which the common people can access productive factors, thereby limiting the accumulation of capital and the re-birth of capitalism. Instead it's sequestered in their isolated communities, which are 'communal' in the sense that any military organization is, and even moreso since as you rightly point out they're essentially tribal communities.
So, the Brotherhood could in this light be considered Utopian, Primitivist, and Neo-Feudal socialists. Utopian insofar as their ideological programme is based upon normative ideals rather than any concrete understanding of material processes, and also their social structure could be compared to the utopian socialist communities of the early 19th century at a stretch. Primitivist along two dimensions - one, their communities in some sense recreate the conditions of so-called 'primitive socialism' by their tribal structure. Two, their essential aim is to enforce primitivism upon others by seizing and controlling advanced factors of production, with the possibility that eventually those factors will be shared and doled out in a 'responsible' manner that avoids the pitfalls of the old industrial era. Finally (and probably the biggest stretch of these stretches) they're Neo-Feudal insofar as they justify and style themselves after the pre-capitalist mode of production, essentially seeing it as better than what followed it.
All of that said... it's still a pretty silly argument, and I'm sure Tagziel just meant "Durr, they share so that makes them gommunist." Beyond that, I don't think it's the most interesting or insightful way of looking at the Brotherhood, and (as is often the case in my opinion for a lot of Marxist analyses) it bears little relation to reality or the Brotherhood's self-conception. But I think this is probably how a Marxist historian in the Fallout universe would analyze the Brotherhood.
EDIT: Misused 'productive factors' completely, want to acknowledge