Almost overnight the Glorious Loyalty Oath Crusade was in full flower, and Captain Black was enraptured to discover himself spearheading it. He had really hit on something. All the enlisted men and officers on combat duty had to sign a loyalty oath to get their map cases from the intelligence tent, a second loyalty oath to receive their flak suits and parachutes from the parachute tent, a third loyalty oath for Lieutenant Balkington, the motor vehicle officer, to be allowed to ride from the squadron to the airfield in one of the trucks. Every time they turned around there was another loyalty oath to be signed. They signed a loyalty oath to get their pay from the finance officer, to obtain their PX supplies, to have their hair cut by the Italian barbers. To Captain Black, every officer who supported his Glorious Loyalty Oath Crusade was a competitor, and he planned and plotted twenty-four hours a day to keep one step ahead. He would stand second to none in his devotion to country. When other officers had followed his urging and introduced loyalty oaths of their own, he went them once better by making every son of a bitch who came to his intelligence tent sign two loyalty oaths, then three, then four; then he introduced the pledge of allegiance, and after that "The Star-Spangled Banner," one chorus, two choruses, three choruses, four choruses. Each time Captain Black forged ahead of his competitors, he swung upon them scornfully for their failure to follow his example. Each time they followed his example, he retreated with concern and racked his brain for some new stratagem that would enable him to turn upon them scornfully again. Without realizing how it had come about, the combat men in the squadron discovered themselves dominated by the administrators appointed to serve them. They were bullied, insulted, harassed, and shoved about all day long by one after the other. When they voiced objection, Captain Black replied that people who were loyal would not mind signing all the loyalty oaths they had to. To anyone who questioned the effectiveness of the loyalty oaths, he replied that people who really did owe allegiance to their country would be proud to pledge it as often as he forced them to. And to anyone who questioned the morality, he replied that "The Star-Spangled Banner" was the greatest piece of music ever composed. The more loyalty oaths a person signed, the more loyal he was; to Captain Black it was as simple as that, and he had Corporal Kolodny sign hundreds with his name each day so that he could always prove he was more loyal than anyone else.
"The important thing is to keep them pledging," he explained to his cohorts. "It doesn't matter whether they mean it or not. That's why they make little kids pledge allegiance even before they know what 'pledge' and 'allegiance' mean." --From "Catch-22," by Joseph Heller
It is his inalienable right to not sign a loyalty oath. He is (was) free to chose a career that does not require affirming one's dedication to all principles of our Constitutional Republic and economic system. He benefited from our system and in returned he provided much entertainment.
As a member of the teaching profession however he would not have had the inalienable rights to indoctrinate students, IMO. Students have inalienable rights too as do the parents paying the bills.