People are saying to wear a hi-vis during demonstrations... Stupid idea IMO. Unless you want to be mistaken for someone connected to the demonstration.
If you wear something that says media / press. You will most likely be questioned to where you work by the organizers. Even if you don't have meda / press you'll still probably be asked. If you have MEDIA written on a jacket, and someone asks what outlet you shoot for. Saying you're shooting for personal interests will be very odd.
Last Saturday in Seattle during the Palestine protest. There were 6 street photographers, 3 or 4 press photographers, and a handful of other photographers that I've never talked to so I don't know who they are.
You'll always be anxious, until you do it. I have social anxiety, and pretty introverted. It was nerve racking the first few times I went out. Once you do it, you'll realize you've made it all up in your head. Do it enough you'll eventually have a bad experience.
Normally people at large public events want to be photographed. Protests want to be photographed to get their message out. Most likely you'll be thanked for showing up.
Here is an example of what I'm trying to get across.
https://i.imgur.com/moRiGA1.jpg
Everyone in that picture with hi-vis vest is with the group as security. NLG just wears hi-vis hats. If you have a hi-vis vest on here. You'll be identified as a protestor / part of the security team. Maybe they don't where you live. But you'll have to show up and verify that your self.
Gotcha. I've never been in that situation. That feels like something where you should ask before going into the DMZ. If you do get it, get the shot and get out quickly.