It can be music about animals, anthropomorphic animals or music from a furry.
At the moment people of "The Fauna Project" are working on a CD containing "furry music". Like "King of your pride" which is a song about a fox and a lioness or "City fox" or "Never cry wolf", etc.
The Fauna Project are people from Germany, Sweden and Austria who love to make music.
Back in 2007, on Eurofurence 13, they performed in the Ringberghotel in Suhl (it was part of the convention).
But calling music furry or non-furry is a bit strange ...