Shooting rioters is exactly what sane rational governments do. Especially arsonists and violent rioters.
Not shooting violent rioters is how you get more violent rioters.
I will now explain when, under our law, a person is justified in using deadly physical force to prevent or terminate arson or an attempted arson.
NY Law: https://www.nycourts.gov/judges/cji/1-General/Defenses/CJI2d.Justification.Arson_35.20%281%29-%282%29.pdf