I think they are mainly referring to psychological testing to determine "fanaticism" in general that would preclude a person from serving in the military (Its not so much about any specific things this person may or may not agree with).
Example: A candidate is stockpiling water, can foods, soups, etc. in their homemade bunker to prepare for "the big one" (whatever "big one" is coming
), they are telling their coworkers, friends, etc. to do the same (Its not that this person is wrong or is doing anything illegal or bad... Its that this person has a psychological tendency to be a "fanatic" and if given the weapons and duty of placing this mind into war....the risks are greater for him/her to "flip a lid" and go "off the deep end" so to speak... much like the recent convictions of that guy that tore up woman and children during battle or that guy that went ballistic at the military base.
In other words I think Its more about psych testing than whether or not someone believes in Independence or our constitution, etc. (I'm not sure if I'm able to explain what im trying to say