The silent movie The Lotus Eater was released on November 27, 1921. Some scenes were filmed on California's Catalina Island.
A portion of the story takes place on an island in the Pacific Ocean where the inhabitants are shipwrecked folk who decide to stay on the island and traipse around in Grecian robes. (Sounds pretty good to me these days.)
This appears to be a lost film, and maybe that's fine with the islanders. ?