Assuming that the EO passes judicial muster, (a big if), the airlines have an easy out. They can segregate their Govt contractual duties from their consumer duties. They can designate specific air crews to government airline usage such as cargo movement and troop movement and designate specific aircraft and terminals, hangers and warehouses to those contracts. The consumer side is going to follow the Taxes EO, (and law if passed), causing a “separation of GOVT and CONSUMER”. As for govt employees: they are consumers which are given discounted tickets, (just as a large group traveling to a convention together and booked together).
That would probably require 2 legal business entities, one fed, one non fed, under a parent holding company. Not trivial to setup.