Some of the rioters are victims, so I'll be upset with all kinds of people.
In general, it's somewhat irrelevant whether someone declares themselves to be press because there are scant laws that declare the press is allowed to do X while a normal citizen can't. The "PRESS" signage should, in theory, be a useful signal to law enforcement that someone isn't there to make a disturbance (this, of course, breaks down if rioters mis-apply the label, but the end result is they endanger the press more than benefit themselves, since the cops can arrest a person breaking the law whether or not they have a particular symbol on their uniform).
Regarding "be a useful signal to law enforcement that someone isn't there to make a disturbance , and also regarding the notion that anyone could slap a press sign on themselves... seems apparent that, to a certain extent, there's an amount of civilization's underpinnings assume well-intent.
In general, it's somewhat irrelevant whether someone declares themselves to be press because there are scant laws that declare the press is allowed to do X while a normal citizen can't. The "PRESS" signage should, in theory, be a useful signal to law enforcement that someone isn't there to make a disturbance (this, of course, breaks down if rioters mis-apply the label, but the end result is they endanger the press more than benefit themselves, since the cops can arrest a person breaking the law whether or not they have a particular symbol on their uniform).