"...a occupying force cares a little bit less than one might first assume"
I don't mean to be overly critical of your imprecise language, but in this context I think it is important to note that a "force" does not care at all. More to the point, a military force comprises individuals who hold a whole range of opinions and who may act in ways that are contrary to those opinions.
"Out of curiosity, do people who grow up under this sort of regime end up thinking it's normal, similarly to the way people raised in Christianity end up desensitized to the absurd-sounding nature of the beliefs about virgin birth and so on? Does it cause them to e.g. be more accepting of government regulation than average?"
Why not look at relatively more secular western Europe versus the relatively more religious US and see which population is more accepting of government regulations. That is to say that either you have it precisely backwards or there is no observable correlation.
"Josh Stieber's fellow soldiers did not change their minds about whether they should be in Iraq."
None of us has any idea whether or not they changes their minds about anything. A soldier can hold a fully-formed (and informed) negative opinion about the strategic efficacy of their mission, but still follow orders and complete that mission.