4th Amendment does not apply.
No one is compelled to submit to any of the security at airports. If you don't want to be searched, don't fly. The 4th Amendment specifically guards against a search that you have no choice in such as a police officer randomly deciding to search you when he sees you walking about. If you refuse, then you will be arrested. In the case of airport security, there is no such threat. Be searched or leave. You don't have to go home, but you can't stay here.