I will rule out military, because we are talking about flying. The military WILL kick you out when you are still in your prime earning years unless you get promoted to General or Admiral...and senior officers almost never get to fly airplanes.

I would say FDX/UPS are safest...they have rock solid business models, provide an indispensible service, and more importantly, the barriers to entry for anyone wanting to compete are astronomically high. Anyone with $100M can start up a low cost passenger airline, but a global package delivery service would require tens of billions of dollars in startup costs, plus untold political and regulatory hurdles in hundreds of different nations. The only real hazard here is automation...but the technical and regulatory hurdles are so large that this is probably not a danger in our working lifetimes. But the cargo airlines will get automated before the pax guys.

Next safest would be US government civilian pilot jobs...but the problem here is that the government could easily eliminate or outsource almost any of the current programs. The safest would probabaly be the FAA...you usually can't privatize the law enforcement.

Out of the passenger airlines, probably SWA. Even they are not furlough-proof in the event of a catastrophe, but it is highly likely that they will remain in business for the forseeable future so you will get recalled eventually. Any of the other pax airlines could easily end up liquidated.