I used to listen to a radio show hosted by a law professor and iirc he said that airport security doesn't violate the privacy amendment because you don't have to fly. When you choose to fly you implicitly wave those rights. How is this different?
9th Circuit Court rules on U.S. vs Davis, 482 F.2d 893, 908... airport screenings are considered to be administrative searches because they are conducted as part of a general regulatory scheme, where the essential administrative purpose is to prevent the carrying of weapons or explosives aboard aircraft ... are allowed if no more intrusive or intensive than necessary, in light of current technology, to detect weapons or explosives, confined in good faith to that purpose, and passengers may avoid the search by electing not to fly
Probably buried in a clause in your carrier contract. Don't fly commercial (fly your own plane or charter through general aviation not CAT, commercial air transport) and you can avoid searches.
