These set a series of variables with each path (Moon/Sun/Tide)
Right now the changes are:
Moon state: Cat Interviewer Tam Void's chest in the Intro is smaller for full moon and bigger for new moon due to the consequences of those paths in the first game.
Sun State: (None yet)
Tide State: Currently determines which story Sister Tim will show you after reading holy text.
In the future you can expect these to:
Moon: Change the appearance and dialogue centered around Albero Verde's Moon Elves, Fox, and Domestic Shorthair (Like with Tam Void)
Sun: Changes whether an Eclipse Elf or Sun Elf Android confronts the player later in the game. This character will speak and act differently but the end result of her encounter will always be the same.
Tide: Has the least impact; only affecting the holy text already in the game and some knowledge dependencies for the story's events for mermaids and Fertility Goddesses.