Private Sector
The issue of constitutionality pertains, generally, to governmental entities. Flying as a passenger is a private sector issue. As such, the companies have the right to refuse boarding and/or handling of bags/freight.
The company chooses how to handle the boarding of passengers. If they wanted to make us strip down before we utilized the service they are providing, the airline could demand such actions. (Note: This is a hypothetical......)
With respect to the discussion of Terry v Ohio, why did I utilize the case for this discussion? It was decided by the US Supreme Court, upheld numerous times, and is the law regarding "searches of individuals." Yes, the facts are different...a police officer (government function) searching an individual on the street versus a passenger being searched in order to board an airplane.
What I see missing in these discussions is the purpose of the search -- access to aircraft. (Now, if you want to discuss the disparate treatment of mechanics, a/c services personnel, etc. versus flight crews, well..........).
The airline has the final authority (or should I say the Captain ...I'm digressing....looks like the American Airlines Captain versus the Secret Service Agent is beginning to heat up via legal channels.....) to decide who they will or will not board.
The whole argument about constitutionality is irrelevant with respect to security searches at the airport -- it isn't a government function. Talking out of both sides of my mouth? (I haven't read the recent legislation regarding federalizing, etc. However, I have faith that it will be attacked constitutionally in the courts, and will survive, in a meandering way, the legal attacks.)
If you want to fly on [insert name of company] airline, then that airline has the right, responsibility, and authority to decide who they will or will not permit access to the aircraft.
FYI: If anyone is interested in "landmark" cases decided by the Court, I would suggest picking up "May it Please the Court...." It is a great overview of arguments presented with respect to some of the more recent/popular issues addressing the Court. For example, the Miranda case is discussed as well as reverse discrimination.
Or, spend three years in law school.....pass the bar....and decide that flying a Learjet is cool....