But, this wasn't "various unrest." This was an occupied, hostile city during full-scale, bloody war. It was a large, economically and strategically important city, vital to the prosecution of that war, and that, during those first nine months of occupation, seemed imminently in danger of rebel attack.
And, as I said, Butler's actions were targeted on those who openly supported the rebellion .... and who were thereby very much guilty of an offense they did commit -- at least in the eyes of the Union, which being in charge, was the sole arbiter.
Yes, the pro-Confederate people of NO were trapped. And they were humiliated, feeling that they had been betrayed by their own defenders, who had surrendered the forts down river after meagre resistance, and then silently slipped out of the city as the Federals marched in, unopposed. And they were humiliated that the CSA had decided they weren't worth the effort to come to their relief. They had not been conquered ... they had been abandoned, and that made the occupation doubly hard for them to bear.