Our public law enforcement operates in the open in the US. They're subject to nearly unlimited public scrutiny, and there is no law that restricts thorough documentation of law enforcement activities by anyone, citizens, suspects, media, etc. It's our main check against law enforcement abuse. Maybe the protestor was going to take the plate number to her lawyer for use as evidence against the department of State Security for abuses of power. But that cop prevented the lawful collection and documentation of information/evidence that was already in the public domain (a license plate in the middle of the street). That opens up a whole can of whoop-a** on that cop and his organization beyond unlawful arrest, as they basically intervened to destroy evidence.
The cop's defense of course is that citizens are not allowed to interfere with ongoing investigations, and they can do pretty much whatever they want if they think anyone is interfering with an ongoing investigation. That is how police in the "real world" can keep gangs from assigning kids to shadow cops with a bullhorn shouting "the guy in front of me is an undercover cop" over and over. Interference with legit law enforcement efforts is not protected. In this case, that justification is pretty much bogus as the SS detective was out in the open covering a public event, and hopefully that will come out in court.
I hope the ACLU pulls out the big guns on this.