No, I wouldn't say it makes you a furry, and I certainly wouldn't say it makes you a sexual deviant.
A furry is someone who is part of the furry fandom, the global community of fans who love and appreciate anthropomorphic cartoon animal characters and the creative, talented artists behind them. Those anthro animal characters are also called furries; Bugs Bunny and Donald Duck are classic examples of furries/furry characters. I don't know whether or not people (particularly those in the furry fandom) would consider the alien creatures in Avatar to be furries. They do have nonhuman bodies and have human-like behaviors, thoughts, speech, society, and anatomy such as hands, body shape, and somewhat similar faces. However, rather than being what would traditionally be considered an animal having human-like qualities (or put another way, an animal with human attributes applied to it), they are aliens from another planet who had those traits all along. Some may call them furries since they are nonhuman creatures with human-like qualities, and some may say they're not furries since they're unlike anything that exists on this planet.
Anyway, as far as your being aroused by their sex scenes (I haven't seen the movie to know what that entails), don't worry about it. However the methods that they have sex and share pleasure, they were creatures, presumably in love, sharing sexual pleasure together. That mental association of seeing other beings sharing the pleasures of sex with the stimulation of sex itself is perfectly normal and common.
"Blue Alien" is incorrect in his/her assumptions about the furry fandom. Being a furry is not a fetish by any means; it is an interest and hobby about the enjoyment of cartoon animal characters. And while some people do have an animal costume (we call it a fursuit), that's certainly not a requirement to be a furry. Current stats, based on furry convention attendance vs. the number of fursuiters in the convention's fursuit parade, show it's about 20% or 1/5 of furries have fursuits. The majority don't have them because they don't want one or can't afford one (they can be very expensive), or just haven't gotten one yet.