First, are there circumstances in which a citizen could apply lethal force to protect life and limb? Obviously yes; shooting someone trying to light your house on fire is certainly something that is both plausible and plausibly legal.
Second, is it appropriate for the political leader of a nation to imply that people committing a crime will be shot for it on the street? Not "we will deploy the national guard to provide safety and security to the citizens" but "looters will be shot". I think the answer here is obviously no, that is not appropriate.
I will also add that this is also a case of tensions boiling over. While that doesn’t justify the arson, meaningful reform to defuse long standing tensions would be a wise move.
You’re right, everyone’s on edge, which has people acting funny.