That is incorrect. Legally under the Air Carrier Access Act, ESAs are protected as well as service animals. Service dogs do not need to have specific paperwork. Now, most airlines do require you submit specific paperwork for ESAs and psychiatric service animals. Some have limited ESAs to flights less than 8 hours. They cannot decide "actually, we don't want this ESA on the plane" willy nilly though. They can still dismiss an animal for behavior or if they cannot fit at your feet without impinging on other pasengers/asle space
More concerning than the flight time, for me, would be the extensive quarantine procedure animals coming from the mainland must go through to enter Hawaii. Service animals can be pushed through with very specific paperwork, but ESAs are not included in this, and it is a tough process even for service animals.