Is it true that you get exposed to a significant amount of radiation by flying on a regular basis?

Not to worry: Airplanes are not shielded from cosmic radiation. Our atmosphere protects us, but because airliners fly at high altitudes, airline crews do get a little more radiation each year than surface dwellers. The amount of radiation per flight is small, so travelers need not worry. A 7-hour flight is about 0.06 millisieverts, the same as 1 chest x-ray (one's annual recommended maximum is 1.0 millisievert).

No: No aircraft, especially commercial aircraft are not "hardened" against radiation, mainly because they don't fly high enough to receive substantial radiation from the sun or space. Even the supersonic concorde wasn't specifically protected since the amount of time it spent over 50-60, 000 ft was relatively short.