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Let me guess, you're American, and this new phone is your first GSM phone? All GSM phones do this, your previous ones were probably CDMA. I'm afraid you just have to get used to it, it tends to interfere with just about any unbalanced, unshielded connection (at low frequencies, at least that's where you notice it).
I have also absolutely no idea if it would be dangerous on an aeroplane, however, the particular problem you describe can often be removed from audio equipment by using balanced connections, you could probably apply the same principles to the aircraft equipment, to deal with that particular type of noise.