Again I have difficulty with the issue on its face. I doubt I will ever answer the question of government restriction on assembly to my own satisfaction.
But if a group who has applied for the permit has potential protesters clamoring for more than peaceful assembly, that probably does not bode well for its case overall. NYC is worried about security and disruption. I don't see how United for Peace can dispel those fears.
Then again when is the next new moon? For all this protesting may become academic. For when America is at war there are few options available to those who dissented beforehand.