Clueless.

In my experience, groups like this have a fairly hostile relationship to State Communism as well. The Kronstadt rebellion for example is frequently cited [1]. But then you have groupings like Anarchist communists [2], which you would then risk lumping together with the anti-Communism part (not to mention that anti-Communism as a term is usually associated with forces staunchly opposed to people like this). Plus, if you are "only" anti-authoritarian, how do you suggest avoiding getting lumped together with Anarcho-capitalism?

[1]: https://en.wikipedia.org/wiki/Kronstadt_rebellion

[2]: https://en.wikipedia.org/wiki/Anarchist_communism

Furthermore, these organisations operate in what they perceive to be Fascist and/or Capitalist societies, so why state opposition to something that is not "there" and has been pretty much gone from the global scene for nearly forty years?

In conclusion, yes, you have a point. But given the reasons above I find it really hard to get worked up over it and Anarchists do not generally get along with Leninists, Stalinists, or Maoists anyway.

Of fascism, capitalism, and communism, only two are going concerns in these people's lives. If they're going to declare themselves "anti-communist" they might as well also take a strong vocal stance against ghosts and flying cars.