The Headroom Between Mutualism and Anarcho-capitalism
I find it inaccurate to use either the terms "anarcho-capitalism" or "mutualism" to describe my own viewpoint. Being a pluralist as well as a person with a fairly complex and subtle heirarchy of preferances that may situationally change, I don't accept either of the two as a singular system that everyone is expected to be a part of. In some ways it could be said that I feel somewhere in between the two.
In the sense that I endorse it, I define private property in an ethical sense as the natural product of labor and voluntary exchange or gift. Anything being called "private property" beyond this I see as a fraud. I do not accept "private property" in a purely legalistic sense, as in whatever the state happens to call "private", thus I draw clear distinction between the status quo of property titles and property rights or a legitimate claim to property. Neither do I necessarily accept "private property" if the term is used to refer to any property that happens to be exclusively controlled, as stolen property and state property can be and is exclusively controlled.
I think that there is a lot of stupid semantics over private property and that those who claim to oppose private property most often actually support some limited or particular form of it but they call it by some other name such as "personal property" or "possessions". I think that in particular situations there can be some kind of private commons or private property that has a policy that effectively makes it "public" in a meaningful sense (see Roderick Long for an exposition on this concept).
I interpret Proudhon subtley. On one hand, I think that it is a misconception to interpret "property is theft" as an absolute statement either pro or con (indeed, taken at face value such a statement is logically incoherant, since the concept of theft relies on the concept of legitimate ownership in order to make any sense), as it has two corrolaries: "property is impossible" and "property is liberty". Each statement refers to a particular context. Socialists who grab onto "property is theft" as an absolute statement against private property are misreading Proudhon, as it refers more to property in the context of an arbitrary legal privilege that can be traced back to thefts than anything else, and they are ignoring the contexts in which Proudhon quite blatantly endorses private property as the only meaningful counterweight to the state.
This position is, in theory, consistant with both mutualism and what's called "anarcho-capitalism", hence making mutualism and "anarcho-capitalism" not as far off as some may like to think. In terms of the labor theory of property (as opposed to value), the two are in total agreement and only disagree in terms of terminology. Wherein they meaningfully differ is in the accessement of what the outcome of freedom of association with respect to property allocation would tend to be. I honestly find myself somewhere in the middle of the two accessments.
On one hand, I do not see anarcho-capitalism as a uniform model, I do not think that a free market would be dominated by a small number of centralized and vertically integrated incorporated firms, I see a possible role for voluntary labor unions as a simple form of collective bargaining, I see the possibility of more individual propietorship and the expansion of enterprenuership, and I see some co-ops as a possibility. On the other hand, I don't see mutualism as a uniform model either, I think that some of the mutualist questioning of the division of labor is misguided or silly and I reject the labor theory of value.
Overall, I do think that the natural of an outcome of a free market would result in an increase in prosperity across the board that could be construed as somewhat egalitarian (in comparison to the status quo at least). Of course, I don't think that it would lead to absolute equality of wealth or ownership in any absolute or consistant sense (nor would I find such a scenario desirable at all), but I do think that workers and consumers would be greatly benefited and in some ways labor would gain much more bargaining power relative to capital. I do not think that wealth being concentrated in the hands of a small few while the majority of people are just above the substinance level is the natural outcome of a free economy, nor do I find such a scenario desirable.
In short, I don't take a doctrinaire approach to either of these ideologies. I value them both enough to synthesize attributes of both of them into my worldview.