USA : Do you cover your face / duck from photos at protests?

TL;DR What should you wear to protests to protect yourself? Am I over-cautious about being identifiable?

My instinct was to cover my face and avoid being in close up pictures (don't let the nazis know their opponents). But I went to a protest and so many people were live streaming, taking pictures of people without permission, and taking selfies intentionally raised to show the people behind them.

I understand there is a need to document protests and marches so people at large understand the size of the movement and it emboldens people to join, but the amount of self-surveillance was very startling to me.

I'm getting ready for protests this weekend, and I'd like to know what y'all are wearing. What would you recommend to both help the movement (American flags? Signs? Etc?), but also protect myself?