Well, it's not exactly a big deal.
Yes, there's a lot of furry haters on the internet, but to be truthful most people in real life don't even know what furry is.
Just relax a bit, it's just like any other hobby.
I think phrasing is important though. Saying "I'm a furry" has more impact than "I have an interest in anthromorphic characters."
Saying "I'm a furry" would make people think that it's more important or harmful than it actually is, and it'll blow everything out of proportion.
Saying "I have an interest in anthromorphic characters" would be better in my opinion, since it doesn't hold the situation as such a big deal and softens the blow, so to speak. It lets people know without making them look at you differently if they don't know what furry is. And in my experience it doesn't rouse as bad of a response from furry haters as the before-mentioned phrasing.
I hope that's helpful to you.
Good luck