No, not for that fact alone. Anyone can enjoy furry porn. Being a furry means you are a fan of anthropomorphic cartoon animal characters and enjoy seeing them wherever you happen to find them. It's more than just liking to see them on TV and in the movies, but is about appreciating them wherever they appear in media, advertising, literature, costumes, puppetry, artwork, sculpture, music, and so on. There are people who are furries who don't like furry porn, so clearly liking porn doesn't make you a furry.
There's nothing wrong with liking furry porn, and nothing wrong with it if you like it better than real life porn. (Personally I very rarely look at real porn because all it does is make me laugh because of how ridiculous the acting and vocalizations are, with all the nonstop moaning even when they're changing positions and not having sex at that moment; on the rare occasions I watch real porn I have the sound muted). Look at what you enjoy and enjoy what you look at. Don't worry about it.