Being a fur is just a way of thinking, it's just who you are regardless of your job.
Having said that, when I was in the Army I was more into Amtgard(LARP) then I was into Furry Fandom(no easy access to a computer), and I will tell you that I got no end of crap for it(purple leather armor, silver puffy sleeve shirt, boffer weapons), but I learned that you have to be who you are, and as long as you were doing your job that can't say anything about what you do on your off time.
Now that I am in the Air Force, and more open about my Furry side, I let them laugh, heck I laugh with them, I answer the questions, I show them sites, I let them come up with there own thoughts on the subject, but the second it becomes harassment I tell them to cut it out and there are things I keep to myself. People will ridicule things they think are silly, and if you think about it we are kinda silly,(I am really silly and it only has a little to do with my Furry side) you just have to be better then them, and if it gets to be too much, handle it, don't just sit on it.
Sorry (Climbs off the soap box), just my two.