I think the purple rabbit phenomenon is just a coincidence in this case. There are plenty of fluffy rabbits that are pink and blue etc in children's stories. Theyre just eye catching and stimulating for the target audience.
As for Zelda, well Ravio is a reference to ALttP where Link turned into a pink haired rabbit in the Dark World.
The reason for this is because Link has pink hair in-game.
He has pink hair because of something like the colour-scheme not working for a natural hair colour because of the terrain or limited colours the SNES could use.
As for Nabbit and Furi rabbit... purple is just a cool colour?