That "if" does a lot of work, as you allude to, and also happens to be relevant to the text I linked since it turns out politics and economics aren't separable except as mental abstractions. I'm not a communist because I want co-ops (I think they are fine but overrated by radlibs and a small number of leftists), I'm a communist because I believe the class that should control the state should be the proletariat (by means of democracy, since they are the vast majority) rather than the bourgeoisie (who control it in neoliberal states by buying out politicians and media), and "ownership" of the means of production is secondary to this. The proletariat controls what the bourgeoisie "own" if the proletariat controls the state and use it against the bourgeoisie such that the latter only persist as a class at the convenience of the former.

I don't see how you think the economic system doesn't matter? That's a BIG if