Washington, D.C., is filled with journalists. Here's a primer on filming police and soldiers in public places - Poynter
Briefly

National Guard troops are patrolling Washington, D.C., and residents are protesting, raising the possibility of confrontations. Everyone has the same right to free speech in public places, including sidewalks, streets, Metro stations, parks, and government buildings. That right includes taking pictures and recording video. Some public places have specific rules against filming, but generally photography and audio/video recording in public are protected. D.C. law allows one-party consent for audio recording, so the recorder can be the consenting party. Journalists do not have to identify themselves in public, and Metro Police policy recommends officer identification but does not make it law. If instructed to stop filming in public, officers are out of line, though practical options may be limited and moving where others stand can reduce confrontation.
Public spaces are generally fair game. Some places, like courthouses and swimming pools, have rules against filming. But unless otherwise posted by the proper authority, taking photos and recording video and audio in public is a form of free speech. If someone, even law enforcement, claims that you need their permission to record audio, D.C. law stipulates one-party consent, meaning that only one person needs to agree to be recorded. That person can be the person holding the camera or recording device.
You do not have to identify yourself as a journalist when working in public. But if you are talking to a private citizen and planning to use an image or their quotes, you should tell them that you are a reporter and that you would like to quote them. The D.C. Metro Police Department has a policy that instructs officers to be publicly identifiable when working, unless specifically under cover. But that's a best practice, not a law.
If a police officer instructs you to stop filming in a public place, he or she is out of line. But that doesn't mean you will win the argument. If an officer tells you that you are obstructing police business by standing in a public space, you don't have much recourse in the moment. Try to find a place where other people are standing that is out of the way.
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