What is funnier than people on both sides of an argument taking themselves way too seriously, and engaging in a bunch of troll-on-troll action?
If looters know that if they don't obey to orders nobody will punish them, that's flat-out enabling such behaviour. People who are willing to loot don't care about niceties, they're just looking for opportunities.
The main problem is that "loot/shoot" could be abused by shooting peaceful protesters and we need safeguards to clearly separate protesters from looters.
However, IMO it's on protesters to single out looters, stop them and, ideally, give them to police. In my country, it's usual for protest organisers (legal or not) to make a point that any bad behaviour will be reported to police and they'll do whatever they can to help out police. Thus police is more relaxed and thugs don't have as many opportunities. If the crowd would be defending thugs.. Well, now that is "glorifying violence" :/