Yes, I think it's possible to appreciate both sides of the issue. In my view, "mutualism" doesn't necessarily include a dogmatic approach to the theory of value either way, and most modern mutualists certainly don't subscribe to the original labor theory of value in its pure form. Kevin Carson has written somewhat of a synthesis of the two theories of value that I'm still reading through.
To me, mutualism is a free market ideology that understands the radical implications of the free market. Mutualists believe that a large percentage - larger than the typical anarcho-capitalist perceives - of economic institutions would either not exist or would exist in radically different forms if the state was removed from the picture. Mutualists, in my view, have a more complete understanding of how the state has warped the development of our economic system. They also tend to hold more culturally-leftist views, to which I also subscribe, and believe that property rights per se are not sacrosanct but rather that they must be determined through a rule/norm creation process in the absence of a centralized legal authority.
In truth I suppose I am sort of a panarchist, but I see mutualism as the next logical step in my intellectual development from conservative-libertarian-ancap.