It is difficult to believe it now but Bengal cats are controversial in some places for the single reason that they are wild cat hybrids. They have Asiatic leopard cat DNA in them to varying degrees depending on their filial – how many generations they are from the wild.
Some people don’t like the concept of wild cat hybrids and some authorities have turned this belief into law. New York City administrators obviously decided that they should be prohibited in their city. They are also banned in Hawaii, and Australia has a troubled relationship with wild cat hybrid domestic cats. Fifth filial (F5) Bengal cats are allowed in Australia. Martin and Kathryn Stucki, former owners of A1 Savannahs tried to introduce Savannah cats into Australia without success. The authorities there are terrified of wild cat hybrids escaping, becoming feral and spawning super feral cats killing masses more wildlife to compound their perceived existing problem.
The fifth filial (five generations from the wild) Bengal cats are considered the same as any other domestic cat because the amount of Asiatic leopard cat DNA in them is so slight as to make only a small difference to their character. However the higher filials were and are considered by some to be too wild in their nature to be suitable as “pets”. This is the controversial aspect of the Bengal cat and other wild cat hybrids such as the Savannah cat.
The bottom line reason why Bengal cats are illegal in NYC is because the people in charge of running this grand city believe that they are unsuited to be companion animals in the city. That’s a tough line to take because, as mentioned, F5 Bengal cats are like any other domestic cat. Savannah cats are also banned, as I recall.
Remember though that policies can change. Perhaps in several years this post will have become entirely redundant because an incoming city administration will have taken a different viewpoint.
F1-F4 Bengal cats are regulated in New York State according to Wikipedia. The same applies to the US states of Georgia, Massachusetts, Delaware, Connecticut, and Indiana. But in these states F5s are fine. But note: laws change. Please check before adopting.