I don’t think the policy of not taking things off the jet is really at issue here (which everyone agrees is pretty much wrong). What is at issue is to what extent an employer can search an employee’s personal belongings. Especially when such a search might take place off company property (and without probable cause or the assistance of law enforcement investigating an alleged crime).
Different jurisdictions have different laws, and the employment law would defer to the locality of the employment contract in force for the person searched. For example, a SFO based individual would follow civil law of the US and of California.
I know of no CA/EA/CBA provisions delineating negotiated procedures for an employee search. The searches are apparently broadband and random (i.e. without probable cause or reasonable suspicion). The searches are occurring through personal effects and not company property (i.e. looking through a bag or purse and not in a company owned locker). And it sounds like they are happening not on company property itself.
So I see the company once again opening up a minefield. Hopefully a based crew will take them to task if and when this happens to them.