Barbour has been pretty blunt about what he thinks should happen to looters. I think that National Guard troops under Federal orders cannot shoot looters except in self-defense, or to prevent a crime of violence, such as arson. Do they come under State rules when called out by their respective Governors? (he said, imagining the level of force the Mississippi Legislature would authorize against looters.)
From: http://www.globalsecurity.org/military/library/policy/army/accp/mp1004/lsn3.htm
PART D - USE OF FORCE
1. Looters. During civil disturbance, looters present a big problem to law enforcement officials. One problem is telling how much force to use in preventing crimes or making arrests. State law enforcement officials are familiar with the rules and policies of the phrase "use of force." These rules provide that deadly force will only be used to stop a felony or prevent an escape as a last resort. There is no typical looter, sometimes women and children are involved. Looting is usually followed by the burning of buildings so that all records of stolen goods will be destroyed. The federal military forces may use force "reasonably necessary" to prevent arson, but under no circumstances will they fire on looters. Warning shots will NOT be fired because of the potential danger to innocent bystanders. When shooting is necessary, shots will be aimed to wound, not to kill. Riot control agents followed by an arrest is one of the best ways to stop looters.
After the San Francisco earthquake in 1906, so I have read, National Guard troops (or Militia as they may have been called then) didn't hesitate about shooting looters. Different strokes for different centuries, I guess.