It's less communism (which had an extreme class-centric perspective the Qunari lack) and more the general authoritarian collectivism crushing of individualism (in which the identification of the individual and their desires is placed over the collective) and the family unit (the historic enemy and frequent target for infiltration of authoritarian ideologies and states).
Since western liberalism practically reveres individualism and still greatly reveres the ideal family unit, the Qunari are essentially ideological heathens to the normal audience.
Riffing off of this: the anti-individualistic bent arguably places the Qun closer to Italian Fascism than any other notable modern human ideology. This being in a real, historical, ideological sense, not the lazy modern usage of "fascism" as a blanket for all authoritarian right-wing stuff.
Fundamentally, Fascists believe that there is no "self" whatsoever, and that it is impossible to conceive of any individual without society, therefore the individual is essentially irrelevant (or, in some cases, an actively harmful construct). Lines up pretty neatly with the Qun, like Dean said. The sticking point is the issue of the "national will".
For Mussolini, Fascism's end-state was to be achieved through the creation of a state directed by a Leader, who would act as a conduit for the national will. This was, incidentally, very distinct from the "will of the people", because for whatever reason the nation and the people weren't the same thing. On the other hand, anarcho-fascists believed that the state was unnecessary, and that the best way for the national will to be expressed was simply by being [Italians].
The problem here is that it's not clear that qunari divide the world into "nations" as a concept with meaning similar to the Nation in a Fascist framework. Although, apparently qunari recognize the existence of other societies, they do not view these societies as being inherently distinct in a way that can't be overcome through, mmm, education. Does that fit with Fascism? Well, kinda. Italian Fascism didn't possess the blatantly racialist ideology that the Hitlerite Bewegung had. (And yes, they were distinct ideologies, and emphatically so, despite what Allied wartime propagandists or Hannah Arendt would have had people think.) Italy's attempts to establish an African empire were overlaid with standard paternalist-colonialist rhetoric that seemed to indicate that the benighted Ethiopians and Libyans under Italian rule would eventually become "civilized". That could fit easily enough.
Does this lend itself to any insights about the way qunari society functions - or if there is a weakness to exploit? Meh. If you look at real, human history, it's very difficult to find any meaningful objective weaknesses on a societal level, weaknesses that prevent a given state from functioning properly and lead to its downfall. The devil is in the details: of implementation, of personality, of random coincidence and chance. The qunari are more likely to fail with a run of bad military luck, or due to the leadership of incompetent arishoks, than to inherent individualistic tendencies among their people. Likewise, qunari ideological success will probably be down more to context than to intrinsic strengths or weaknesses of their program.