When you get right down to it, I think one of the most important things in the world is to be honest with yourself and with others about who you are. While it's appropriate to behave in certain ways to fit specific situations (i.e., acting in a specific manner when in class or at work as opposed to how you act around your best friends), you should never pretend to be someone or something you're not. It's true that some people (or even a lot of people) might not like what they see, you'll attract the people who will truly love you for who you are.
I'm speaking from personal experience, of course. With regard to being a furry, I'm quite open about it with my close friends. I don't make a huge deal about it of course, but I'll make the occasional furry-related joke or reference in front of them. Usually they'll laugh, or think it's cute, or just have a neutral reaction, which I don't mind at all.
There was one person, though, who was genuinely disturbed by the fact that I was a furry. They actually confronted me about it and asked me what species I identify as. I said human, to which they replied, "Ok. If you had said fox, then we would have had a big problem." (at the time, my fursona was a fox) The short version of the conversation that followed is this: I told them that even if I did want to identify as a fox, that's my own choice, since for many people, that sort of thing (therianthropy) is a serious spiritual matter. And if they couldn't accept that, then I have a big problem with them. The person refused to accept it or try to understand, so I cut them out of my life for good.
Basically, my opinion is this: hold onto the people who love and accept you for who you are, and just forget about the ones that don't. They're not worth your time or energy.