You need to watch the ending in case you missed it:
The surprise twist ending: Nancy has survived the pod invasion, but Matthew did not. The bloodcurling zombie scream he emits is his way of alerting other duplicates to a human presence.
So how does all of this relate to the Cold War? Consider the ways in which Truman's Policy of Containment, as well as the McCarthy Era attempted to identify an "other" as the enemy. Relate your understanding of the film to the historical context. In what ways do you see the American government identifying and rejecting an "other" in their policies? What was the threat posed to American society after the war? Do we still see such fears and threats posed to our society today?