> It's a constitutional right to record them doing their duties, in public. That's clear.

Less clear than it used to be https://en.wikipedia.org/wiki/Mario_Guevara_(journalist)

From the wikipedia article: "Guevara was ordered removed from the United States by an immigration judge in 2012"

The removal case was administratively closed on appeal which meant that he was legally authorized to stay in the US while waiting for a green card application to go through.

He was here on a work permit when the police arrested him for filming a protest. Journalism isn't a crime so all the charges connected to his arrest were dropped, but ICE placed a detainer on him to keep him locked up anyway. A judge granted him bond so that he could be released but ICE fought that too and continued to keep him locked up. Finally they reopened the 2012 case and used that to kick him out of the country.