What happens to opposing viewpoints if AnCap becomes mainstream? It seems that AnCap would start to oppress their opponents. Thus it would no-longer be voluntary - everyone would be forced to do things the AnCap way.
Well, that depends on what you mean by "forced to do things the AnCap way." If you mean forced to operate as capitalists, you would be wrong. If you mean forced to not steal, rape, murder, or coerce, well, then I suppose you would be right. But again, "forcing" someone not to do those things is not coercion, it's defense.
Since the notion of "private property" seems just as much a dogma as the notion of "State ownership", what makes AnCap supporters (and holders of related views such as Libertarianism) think they are more morally right than others?
If you feel "private property" is "dogmatic," then answer me this question: Who owns you? Answer that question - truthfully - and you will see the moral basis for our claims.
Edit: and we haven't even touched on the possibility of a healthy middle-ground like the "real world" has -- with various combinations of a State and private property.
If you can call - with a straight face - the systems currently in place around the globe "healthy," you're either hopelessly deluded, or straight-up evil.