Okay, I don’t mean to be at all rude, but many ancient Mesoamerican cultures would fit the bill as a ‘furry’ today. Many of their high priests wore animal skins as a sign of power given the them from the gods, not to mention the main bro they thought was snazzy was the giant feathered serpent, Quetzalcoatl. That dang snake was all over tons of temples and carvings, truly the Mickey Mouse of the Mesoamerica. And between their different cultures and tribes, almost all of them worshipped jaguars and other animals as gods. If my memory serves me right, I believe it was the Mayans who had the anthropomorphic jaguar god.
:)