I mean you could argue that about Emos, or Goths. Its not really true.
I'm sure sex is a large motivator, but you can't be doing sex all the time. When a Goth is dressed up all Goth-y its not because they are horny right now. They are just wanting to look good.
I imagine its the same with the furries, but the difference is, the furries are the butt of most jokes