I don't think it "supersedes" the conscientious objection, it's a completely different topic altogether. When you talk about "conscientious objection" you're referring to the job
itself, not the employment requirements necessary to have the job in the first place. In the case of the military, both a conscientious objector on KP and an infantryman on the front lines are required to get the vaccine or face discharge. In the case of the FAA, both the line controller and the guys at the District are required to get the vaccine or face dismissal.
A more appropriate situation would be a worker at CVS whose job duties require them to administer the vaccine, but that conflicts with their supposedly-deeply held beliefs. CVS as their employer may offer them the opportunity to perform other work or may fire them for refusing to perform their duties. But in either case the question of whether the employee is themselves vaccinated is not the point:
being vaccinated is not the thing the employee is "objecting" to (though it may well be a separate condition of employment).
Shut the hell up. Unless and until Congress passes a law mandating a state religion (which would violate
the first line of the very first amendment to the Constitution) we are not "under God" and you should feel bad for bringing that up (as should the blowhards who added "under God" to the pledge in the 1950s).