No they didn't. They agreed with the principles and vision. They just disagreed about how to get there.

Nope.

From Proudhon, generally considered the first modern anarchist: "A common danger tends to concord. Communism is the exploitation of the strong by the weak. In Communism, inequality comes from placing mediocrity on a level with excellence."

Want more? Benjamin Tucker (one of the first American Individualist anarchists): "I will simply call attention to the fact that it is an ideal utterly inconsistent with that of those Communists who falsely call themselves Anarchists while at the same time advocating a regime of Archism fully as despotic as that of the State Socialists themselves."

Private property under capitalism is inherent. Hence, incompatible. You're trying to give me a semantic debate where there isn't one.

Private property doesn't have a universal definition, and occurs in degrees -- not all concepts of private property resemble Wal-Mart or Monsanto. Private property is not inherently exploitative unless you are an essentialist, but in reality it's much more fluid. To quote Tucker again: ""I do not agree with Mr. Owen that Anarchism does not commit its adherents to any economic dogma. Anarchism is a word without meaning, unless it includes the liberty of the individual to control his product or whatever his product has brought him through exchange in a free market—that is, private property. Whoever denies private property is of necessity an Archist. This excludes from Anarchism all believers in compulsory Communism. As for the believers in voluntary Communism (of whom there are precious few), they are of necessity believers in the liberty to hold private property, for to pool one's possessions with those of others is nothing more or less than an exercise of proprietorship."

You have private property, you don't have anarchism. It's as clear as day.

Anarchism ought to be defined by the constant skepticism and examination of hierarchical structures on an individual basis -- not some checklist of certain criteria determined by some authority.