Sicarius, I don't think you quite understand capitalism. Anarchy and capitalism are not mutually exclusive and in many ways very complementary. If you leave people to do what they will with no oppressive forces, capitalism is ultimately what results. It doesn't have to be monetary, and you can call it a "gift" economy, but it will always be capitalism. I can understand that you think authority is inherently exploitative and oppressive, but capitalism is not inherently exploitative and oppressive. What sort of economy do you think would arise in an anarchy if not capitalism? Surely any redistribution plan is indicative of authority.
"Capitalism in the sense of wealth accumulation as a result of oppressive and exploitative wage slavery must be abandoned. The enormous differences between the wealthy and the poor do not only cause tensions in society or personal harm to those exploited, but is essentially unjust. Most, if not all, property of today is generated and amassed through the use of force. This cannot be accepted, and no anarchists accept this state of inequality and injustice. As a matter of fact, anarcho-capitalists share this view with other anarchists. Murray N. Rothbard, one of the great philosophers of anarcho-capitalism, used a lot of time and effort to define legitimate property and the generation of value, based upon a notion of “natural rights” (see Murray N. Rothbard’s The Ethics of Liberty). The starting point of Rothbard’s argumentation is every man’s sovereign and full right to himself and his labor. This is the position of property creation shared by both socialists and classical liberals, and is also the shared position of anarchists of different colors. Even the statist capitalist libertarian Robert Nozick claimed contemporary property was unjustly accrued and that a free society, to him a “minimalist state,” needs to make up with this injustice (see Robert Nozick’s “Anarchy, State, Utopia”). Thus it seems anarcho-capitalists agree with Proudhon in that “property is theft,” where it is acquired in an illegitimate manner. But they also agree with Proudhon in that “property is liberty” (See Albert Meltzer’s short analysis of Proudhon’s “property is liberty” in Anarchism: Arguments For and Against, p. 12-13) in the sense that without property, i.e. being robbed of the fruits of one’s actions, one is a slave. Anarcho-capitalists thus advocate the freedom of a stateless society, where each individual has the sovereign right to his body and labor and through this right can pursue his or her own definition of happiness." - Per Bylund, Anarcho-capitalist