Final answer:
During the 1950s, the Cold War hostility did not intensify to a point of uncompromising stance between the U.S. and USSR, as they engaged in pragmatic discussions to prevent conflict escalation.
Step-by-step explanation:
At the height of the Cold War in the 1950s, it is NOT true that the hostility between the U.S. and USSR grew more and more intense and uncompromising, as represented by option B.
While hostility indeed existed and at times relations between the two superpowers were fraught, the superpowers maintained a level of pragmatic communication to avoid an escalation into a direct conflict, evident in the avoidance of a "hot" war and their mutual involvement in diplomatic discussions and arms control agreements designed to mitigate the existential threat of nuclear warfare. The other aspects listed in options A, C, and D such as the reliance on nuclear weapons, completion for allegiance from Third World countries, and the unrest in said countries were indeed characteristics of the Cold War dynamic in that era.