IMHO, as someone that works in security / privacy, I tend not to view it as a binary thing. It depends on where you live, what you’re protesting, what you look like, who you are, etc.
Are you in Russia or China and are protesting the government? Yeah, I might leave that thing at home. Are you a white lady in San Francisco marching with a pink knit cat hat during brunch hours, then you’re probably well on the other side of the risk spectrum. You might actually be introducing more risk by having less immediate access to communication or a camera.