Not the same thing, but in the same vein, and I think I can give you a useful perspective on this. I've told a fair chunk of my family and a number of my friends that I'm a zoophile.

Let me ask you this: Why exactly do you want to tell anyone that you're a furry? What exactly is "being a furry" to you in the first place?

For me, being a zoophile is something fairly major. It affects a good portion of my real life. This isn't generally the case for someone in a "fandom". If "furry" is just a fandom for you, that's probably a sign that you want to keep it to yourself. Likewise, if it's just a fetish, again, people don't generally need to know that.

Basically, if this is something you're really dedicated to, or it's particularly, then maybe you've got a reason. If not, keep it to yourself.

Though it also depends on the sort of relationship you have with whoever you're going to share the info with. If you've got the sort of relationship where you discuss lewd things all the time anyway, then who cares? Not a big deal at that point.