I wouldn't say a hazmat ban is more important than a road with 8'0" bridges, which most NY parkways have. In general, any route with the word "parkway" means stay off of it with the RV. Parkways also do not have route numbers, another way to tell if you shouldn't be on it.
Ones I can remember in and around the NY metro area:
Northern State
Southern State
Cross Island
Sagtikos
Wantagh
Meadowbrook
Interboro
Hutchison River
Cross County
Merritt
Taconic
Palisades
Probably missed one or two...they have really increased the signage in recent years with NO TRUCKS signs. If you find yourself on a parkway in error, pull off to the side ASAP before you get to a low bridge, and wait there for the state guys to come along and write you a ticket and escort you safely off.
There is no hazmat restriction on the parkways, but no towing is allowed, so you will get a ticket if you get caught with a pop up even though you'll make it under the bridges...