I think I've got the four island guardian Pokemon's origins figured out. I mentioned in an earlier post that they seem to be based on the four major Hawaiian gods--Ku, Lono, Kane, and Kinolau--, and that Tapu Koko was the Pokemon equivalent of Ku.
Tapu Bulu appears to represent Lono, the god of music, agriculture, and fertility. The bell on its tail represents music, its Grass typing represents agriculture, and bulls are associated with fertility (at least male fertility) in many cultures. The official site describes that it does not like to fight. This matches with Lono's holiday season Makahiki, a four month harvest celebration during which no war was allowed.
Tapu Fini probably represents Kinolau, the god of the ocean. He is normally depicted as a squid or octopus, but the sailfish design they've given Fini could represent his power over the ocean winds and sailing. Its official description says it protects a purifying water that only those who prove themselves can use. Kinolau was heavily associated with the drink kava, which had many medicinal uses for ancient Hawaiians and was sometimes prohibited to be used by anyone other than kahunas. Fini is also the only Water type of the quartet.
That means Tapu Lele represents Kane, the god of creation and life. This is where things get muddy. Kane brings fresh water and edible plants like taro root, but the Water and Grass typings are already taken by Fini and Bulu. Lele looks like a butterfly but Kane is not associated with butterflies. It could be an allusion to Kane's connection to the sun, sky, and daytime. Kane is also associated with plants as previously mentioned, and butterflies pollinate plants. Lele's healing scales could represent Kane's life-giving powers. Not sure where its Psychic typing comes from. It could refer to the knowledge it took to successfully grow taro roots, or it might just be the old "just make it part Psychic" treatment lots of legendaries get.