Could you please be more specific as I could not find "The one or ones that have been barring what communities don’t want since time immemorial. That one." listed in The Charter, Administrative Code, and Rules of the City of New York.
Look harder. The rules don't change for the Godless cult. NY of ALL places knows how to stop a thing, LEGALLY when they WANT to. NYC stops or micromanages more than it leaves alone or allows. The fact that you don't know how they do it is a shortcoming of yours. Study a little harder is all I can advise. I'll give you a key word: ‘Bureaucracy’ I don't recall any constitutional problems in my 51 years of seeing NYC do as it damn well pleases.
We should all cut to the chase and put up some money on the outcome of this thing, get a big pot going. I honestly believe the Mosque is doomed.