[@ArmorPlated]
Is it a matter of their coexistence? I was under the impression that Hylia was like, the one deity above all, and then Din, Nayru, and Farore were created by and subservient to her. Just in some games she's either so ancient or so unconnected to events that only the three are ever mentioned. Then again I haven't played Skyward Sword which I think is the game in which most of that got hammered out.

As for Hylianism, that could potentially go back to the arguments from way back over different translations of the games--does the word "Hylian" refer only to the race of elf-like people with pointy ears, or does it refer to every citizen of the Kingdom of Hyrule regardless of race? Are a Hylian and a Human the same thing? Is there a difference between Hylian and Hyrulean? Are the people of Ordon village a different race since they have round ears? So on and so forth.