That is exactly how sharia is implemented. You knew that, and presented the scenario, anyhow. Why?
That is a bizarre extrapolation. Vigilantism is a proud American tradition when criminals run rampant, and government either won’t stop them, or worse, joins with them against the honest citizenry. It’s got nothing at all to do with Sharia law, which from the American point of view is something that primitive and barbaric foreigners do.
Vigilantism almost always remains a peaceful movement, following legal means to get the government to perform its duties. But it only arises when those peaceful means are thwarted. This means petitions are despised, elections are subverted, attempts at citizen watch patrols to report crime and criminals are ignored by the police.
As soon as a citizens organization forms, not even imagining itself as a vigilante group, the criminals see it as a threat to their power and attack it, and the government sees it as a greater threat to *their* power than even the criminals and attack it as well. They do this with threats and violence directed against the leaders and members of the group and their families.
This can mean an attack by criminals, or the police, or both against non-violent citizens. And they are not satisfied with just breaking up the citizens group; they want to humiliate it and humble it before its criminal and government masters.
Finally, the citizenry can take no more, and decide to drive out the criminals and likely the corrupt government. And even at this late point, they just want them to leave. But if they resist, then the vigilantes finally turn violent, and become a lynch mob.
Posters like this, that I mentioned before, oddly go up after the criminals and corrupt government have been driven out. The purpose, I suppose, is to let any remaining criminals know that they had better leave, because any attempt by them to break the law will be met with swift punishment.
All of it is US history, repeated many times before, mostly in old California. Nothing at all to do with Muslims and their heathen ways.
So all told, by posting such flyers in a rough part of Chicago, those who know US history would recognize them, and they would be seen as a damning indictment of the local government. And that is the real purpose of the exercise.