To the best of my knowledge, the rivalry portrayed in this film is COMPLETELY FICTIONAL.
I can tell you that my Italian-American grandmother grew up in Little Italy with her family during the 1920s / 1930s, and two of her younger siblings married Chinese from Chinatown. And this was not considered uncommon… Years later when I told my grandmother about this movie (and the way it portrayed gang rivalries between Little Italy and Chinatown), she said she’d never heard of anything like that.
I can also tell you - based on my own experience of visiting the area in the 1980s - that by the time this movie was made, the “neighborhood” of Little Italy had virtually no Italian-American residents left. The area called Little Italy was just four blocks on Mulberry Street of Italian Restaurants and Tourist Shops. The Italian-American workers there did not live close by - they commuted from New Jersey, Staten Island, or Long Island. I clearly remember speaking to several shop owners who clarified this (not just about their own business, but also other businesses in Little Italy). I also happen to remember one Italian Tourist shop which hired a young Asian girl as an employee behind the counter (I always assumed she was a Chinese-American resident of Chinatown, but I never actually asked).
I can also tell you that in the 1980s (and still to this day), Mott Street - the heart of Chinatown - was a big tourist attraction, not a place of gang wars. Tourists visiting Manhattan, not to mention family residents of the outer boroughs, would often go to Mott Street on a Saturday to get a good Chinese meal. It was always a treat to visit Mott Street… My point here is that in the 1980s, BOTH the neighborhoods of Chinatown and Little Italy depended on outsiders to keep their businesses going. Every day and night, people of all different kinds ethnic backgrounds - from all over New York City and all over the world - would walk down these streets, shop in the stores, eat in the restaurants, etc, and they were ALWAYS welcomed by the store owners and local residents.
Bottom line is: the more familiar you are with this area (and its history), the more you realize how fictional this movie is.