I've read a good bit about Buddhism so I'm pretty sure it's not of that religion. I'm at a blank on Shinto though as I've never done any research there.
I know felines are revered by Buddhist culture. Cats were often employed as mice assassins at many temples. As these cats befriended the monks their function as mere mice killers quickly evolved to the more honorable status of protectors and guardians of the temples they were employed at.