The final allegiance of the FBI is to the country and the Constitution, not the President.
It doesn't mean blind and unquestioning obedience. It means putting the interests of your government above yourself. It means doing everything in your power to ensure that your boss is successful in doing his job.
For instance, suppose a commanding officer of a ship runs his ship aground while at the Conn. Sure, he gets fired, but every officer on the ship gets a very good look to ensure that he did everything in his power to prevent the Captain from erring. Did the officer of the deck warn the CO that he was headed for shoal water. DId he push to the limits of disobedience of a direct order and insubordination to convince the CO of another course of action. Did the XO? Did the Navigator? Did officers on watch alert those two of the problem assuming there was time.
That is what loyalty in a military officer demands. It's not unjustifiable obedience. It is dedication to the success of the organization.
I really cannot believe that there is anything wrong in expecting genuine loyalty. It's a fundamental requirement for trust.