I think it comes down to this for non-instrumental pieces. If, without knowing the artist or title of the song, somebody could listen to it and still think it at least related to animals in some way if not to furries directly, I'd say it could be claimed to be 'furry music'. Otherwise no, regardless of the creator's intent or the title of the song. That goes for any fan made music from any genre. The song must speak for itself in other words.
I think it comes down to this for non-instrumental pieces. If, without knowing the artist or title of the song, somebody could listen to it and still think it at least related to animals in some way if not to furries directly, I'd say it could be claimed to be 'furry music'. Otherwise no, regardless of the creator's intent or the title of the song. That goes for any fan made music from any genre. The song must speak for itself in other words.