Ebbie, Classical Guitar is what I have and play. Nylon didn't make any difference on the way there.
Murry, the story of the girl who bought an extra seat than had to store her insturment in the overhead compartment has made some papers. I'm sure if you search, you could find it. But when it comes to airplanes, you either do exactly what security tells you or you don't fly (as examples above will demonstrate). They don't care what you insist on.
Ana, The violin player I met told me to never fly Alaska as I'd have no chance of getting on the plane. I'm glad to hear that your not having those experiences though. Still, I don't see why I should be paying more for an extra seat or insurance just for being a musician. As a student and a musician, I don't have that kind of money.