I highly doubt it. Anarcho-capitalism is far too dysfunctional to ever be a legitimate global ideology. Any society founded on its values would quickly collapse into plain old state-run capitalism, the state being the property owners, or feudalism.
"Self-management societies" aren't an ideology either. You could have self-managed societies operating on a huge number of different ideological foundations, and a large number of those ideologies are represented among the members of this website, so I'm sure they'd be happy to tell you all about that. So if we're talking about a war of ideas, it would be way more complicated than that.
Also, if we're talking about a real, violent war, I don't know about other ideologies as much, but a society built on any kind of truly anarchist foundation would not consider war, other than in self-defense, to be something worth engaging in, and really wouldn't have the infrastructure or political structure to even engage in organized, aggressive warfare. Therefore, if there ever was a war between state-run capitalistic societies and self-managed communities, it would likely be a war of guerilla resistance against organized capitalist aggression.


