I thought I'd throw my two cents in here.
Personally?  I never *tell* anybody I'm furry.  I also never pretend I'm not.  I don't see any point in sitting people down and having some big, drama-laden, deadly-serious discussion about it.  It's just a fandom, why should I make it into some kind of production?  Likewise, it's just a fandom, why should I go out of my way to hide that I'm into it?  I do the furry things that I enjoy, and people will figure it out, or not, and they'll care, or not.  I think that "coming out" about being furry just makes drama where there isn't any.  Just *be* furry and don't make it into this huge deal.