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They most certainly are not. Some right-libertarians have convinced themselves that they are anarchists so that they can pretend to be radicals but that does not make it so. Anarchism and capitalism are incompatible, anarchism is a left-wing ideology that among other things, seeks the end of capitalism.

I don't know why you interpreted my comment as being a criticism of communism or anarcho-syndicalism (it was just a probing question to understand what somebody thought anarchism would look like), and neither does your criticism of those ideologies make much sense. I don't think you actually know what anarcho-syndicalism is if you think it involves party politics.