Yes, but it has to be an imminent threat, i.e. you think you are mere moments away from being killed (or very seriously injured).
The threshold for deadly force should be the same whether you are in law enforcement or a regular Joe.
I used the BLM example because in many cases that was a violent mob.
On of the basic elements of self-defense law is that of
Imminence, meaning that the threat against which the officer was defending was either actually in progress or immediately about to occur.
It was subjectively (and objectively) reasonable for the officer to perceive a “threat” in the form of the mob violently breaching the barricaded doors he was guarding. Once the mob had breached the doors there would be no practical means by which a single officer with a handgun could prevent the protestors from flooding further into the building, and presenting a deadly threat to the (mostly unarmed) other people whom the officer had a duty to defend and protect.
Moreover, the officer was receiving radio reports of protestors making use of chemical agents on officers and of shots being fired into the House chambers and, it is not necessary for these reports to have been true, it is only necessary that the officer had reason to believe them to be true which made his actions even more reasonable.
Just as an individual defending against the mob outside their home should try to be reasonable, as long as the mob remains outside the home. However, mob has forcibly and unlawfully breached the home, the threat against the occupants is clearly imminent. And unlike some states wherein there is a duty to retreat for civilians, the officer's duty is to protect people against such a mob.
The “red line” which when crossed justifies the use of defensive force. In the instance of the Capitol shooting, the barricaded doors Byrd was defending constitute that red line.
He didn't fire into the crowd before or after the breach. But once they smashed through the glass upper panel of the door—then made forcible and unlawful entry iin progress, and the threat—again, that the barricaded doorway the guard is defending will be breached—is actually in progress, it meets the conditions of the element of
Imminence.
So, when Byrd fired the fatal shot into Ms. Babbitt, could he have had a reasonable perception that the doors he was defending were in the process of being breached?
Indeed, a close examination of the screen capture suggests that at the moment the shot is fired Ms. Babbitt has actually breached the door by extending her leg through the window frame of the door.
"Immanence" doesn't require him to only shoot when others follow and are pouring through the door, by then it could be too late (and result in even more tragic deaths).