Shep69, this is from California law (my bolding):
648. "Employment" does not include service performed on or in
connection with a vessel or aircraft not an American vessel or an
American aircraft, if the employee is employed on and in connection
with such vessel or aircraft when outside the United States.
This is interpreted by those more educated on these matters than I as meaning that if the employee EVER does any work on or in connection with the aircraft WHEN outside of the United States, or if the employee MAY be ASSIGNED to do work (i.e. EMPLOYED on or in connection with) on the aircraft WHEN outside of the United States, the exemption applies to ALL work done by the employee. Therefore, any domestic sectors or ground duties would also be exempt.
Also, an employer cannot opt-in to FICA, just like a worker cannot, on his or her own volition, contribute to FICA if he or she performs work which is not considered employment by the FICA laws.
No one in the US or California government said, "Hey! Cathay! Stop sending us money!" However, the intent of the law is that if performance of work is not considered employment, an employer (or an employee) cannot arbitrarily decide to call it work and then contribute to FICA.
I think Cathay is correct in stating that it has no option to continue FICA contributions, even if it wanted to do so. The question remains: what happens to the contributions already made?
SDI is exempted, as well, by California law in the same manner as FICA.