Ugh.
OK, from my vicarious experience with the military (Two brothers in two different branches) the knowledge is very compartmentalized.
Your average GI Joe is not going to have special knowledge of FEMA camps or anything else. In addition, since the military went all-volunteer, the political cross-section of the average American soldier has skewed considerably to the right, and (according to my 'Army' brother) the average intellect has taken a serious nose-dive.
So, considering the above factors, I would say that it would not be all that surprising to find that large numbers of soldiers, especially in the enlisted ranks, would be susceptible to these kinds of beliefs.