For those of you disappointed that they don't get into how these films fit with the Fox News pre-conceived narrative of the world, allow me to try to illustrate how the films I am familiar with could be interpreted to fit that worldview.
SPR: This, like all Spielberg and Hanks WWII projects, is pretty much patriotic in the way Veteran's Day is patriotic: America is the good guy and the good guy is punching a fucking Nazi. Nothing really goes against the Fox News grain there.
Tora! Tora! Tora!: "I fear all we have done is to awaken a sleeping giant and fill him with a terrible resolve." This line is pretty much the mantrum of every geriatric xenophobe and young paranoid nationalist in the country, i.e. the key Fox News demographics.
Full Metal Jacket: Kubrick is consciously trying to neutrally examine the phenomenon of war. In the Fox News mindset, if you aren't against something, then you necessarily must be for it.
M*A*S*H: This one is sort of the only one that I can see being genuinely confused about. I sort of suspect the person or persons who compiled the list never actually watched the film and just assumed it was like the television show.
Letters From Iwo Jima: Notice Flags of our Fathers isn't the one they chose. I agree with that choice, but only because this film is the only one of the two that is actually relevant to our times via the examination of the Japanese. To the Fox News viewer, I can honestly see them viewing this film as a black and white study of suicidal, animalistic Japs mercilessly opposing the forces of good and dragging poor Ken Watanabe along for the ride.
Glory: For the non-neo-Confederate Fox News viewers, Glory simply reaffirms their nationalism. For the neo-Confederate viewers, they can take the film's framing of the conflict as a national tragedy as an indictment of the Yankees.
A Bridge Too Far: This film fits in perfectly with the right-wingers take on every single conflict we have ever lost: they were lost by the "elites." If those fags had kept to themselfs with thar buchlernin' in them ivery towars, we'd be just fine, thank ya very much.
Platoon: Oliver Stone's view of the Vietnam War is surprisingly close to the right-wingers view of that war, i.e. the elites betrayed the soldiers and veterans. They just disagree over what that betrayal consists in and a viewer determined to read his version of that betrayal into the film can.
Black Hawk Down: You read our failure in Somalia as a failure of the test of the Clinton presidency's resolve.
The Deer Hunter: A right-winger could read the film as an indictment of weakness and take the singing at the end at face value.
Paths of Glory: There are two easy ways a Fox News viewer likes this film: 1) You read it as an indictment of the French military and nothing more. 2) You interpret the film as taking the side of the superior officer, not Dax, in the final exchange of the film.
Apocalypse Now!: I love that we actually studied this film in my hometown's college prep courses because I can present exactly how Red State Americans view this film, or at least the ones that read, anyway. They view this film as a study of Hugo Grotius' view of the virtuous warrior, with the Colonel Kurtz character as the paragon of virtue. Seriously.
Schindler's List: A film that deals with the Holocaust head-on allows right-wingers to bask in the mythologized past of a time when you could tell the good guys from the bad by the uniform we wore and we were the unerring good guys.
The Bridge on the River Kwai: This is yet another WWII film that focuses on the barbarism of the Axis, virtue of the Allies, and insanity of the elites on both sides. Again, that fits in perfectly with the anti-intellectual, jingoistic worldview of Fox News.
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