@trash_witch
I think about this a lot. I also do (armed) security for pride events, drag shows, things of that nature. Sometimes that ends up with me in an official looking position wearing some kind of identifying thing, sometimes I'm just a face in the crowd with a concealed carry permit. I don't mind being identifiable at those types of events though, the interactions I've had as a result have been overwhelmingly positive.
I've also done (armed) security for protests a number of times, when asked, but I've quickly learned that I don't like being identifiable in those scenarios at all, for the reasons you mention: an "official"-seeming, deescalating presence isn't good for a protest, it creates a scenario where people feel the need to seek permission of anyone official-looking to do anything remotely different from whatever everyone else is doing. It changes the dynamic of the protest, makes everyone more hesitant to act of their own volition.
However, I live in a place where protesters do get killed on occasion. I saw it happen once. I'm going to keep carrying when I go to protests, especially when I'm specifically asked to. I'd just rather not look like I'm in any kind of official role while I'm doing it.