What NY is mainly worried about (and has the strongest public support for them worrying about) is AirBnB being used as a way of de facto running unlicensed hotels. People don't like discovering that the room down the hall from where they live has essentially been converted into a hotel room, with customers coming and going regularly, no hotel tax paid, and none of the usual health/safety regulations applied (industrial-strength fabric cleaning, etc.). By comparison, someone renting out a spare room now and then is not as likely to produce social or health problems, and most of the public probably views it as benign, even if also technically a violation of your lease.

I don't like this kind of thing as a customer, either. When I look for a place on AirBnB, I expect it to be someone's actual house/apt, which they treat as their own, because they also live there. If that's not the case, it should be made really clear up front.