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The ACLU has published an internal FBI "Domestic Terrorism Operations Unit" publication titled "Anarchist Extremism Overview." It lists a number of First Amendment protected activities that supposedly dangerous anarchists engage in, including "creat[ing] a political statement" and "generat[ing] media coverage for their cause." The presentation is heavily redacted.
In late December 2011 Amy Goodman interviewed Scott Crow, an Austin area anarchist who found out that the FBI had been watching him for a long time. (Someone should tell the FBI that Crow isn't a terrorist.) She also interviewed Mike German, privacy counsel for the ACLU and a former FBI agent who infiltrated white supremacist movements in the US. German explains that under current Justice Department regulations, the FBI is allowed to spy on people like Scott Crow -- or anybody else, for that matter -- without even a shred of evidence suggesting the person is engaged in criminal activity.
The Attorney General of the United States issues rules that dictate the boundaries within which the FBI may conduct its operations, called the Attorney General's Guidelines for domestic operations. The AG has changed its guidelines many times since 9/11, each time granting the FBI more leeway in its investigations and chipping away at hard won privacy and civil liberties protections. The 2011 revision allows agents to start snooping on people without even officially opening the first level of investigation, called an "assessment."
The 2008 AG guidelines so loosened the standards for FBI investigations that they are basically nonexistent. No factual predicate is required. So the idea that agents would be able to start those investigations without even going through the administrative hurdle of opening an assessment is an expansion of power that is completely unaccountable.
Since the government doesn't need any factual predicate before spying on someone, and since it has demonstrated a long term interest in spying on activists and organizers, the Bureau shouldn't be so surprised to learn that anarchists are concerned about their privacy. But in typically self-aware fashion, the FBI says anarchists are just paranoid. Right.
Read more about the conflation of dissent with terrorism.