Answer: the West as a civilization (elites the West) felt threatened by communism a long time before WW II started. When Bolshevik revolution took place (1917) international communist started expanding all over the world. World-wide population was seized by the image of final apocalyptic conflict betwen bourgeoisie (Christian values, western traditions, capitalism) and barbarian Commmunism. All that was based on Marx´s "scientific" prophecy of apocalyptic conflict between two irreconciliable forces of decadent bourgeoisie and progressive proletariat. Mutual animosity existed (even though only theoretical because worldwide Communist revolution never ocurred) also during WW II. The conflict was there. GB and USA collaborated with USSR militarily and politically but it does not mean they adopted Communism or became permissive towards it. After the WW II what we call "division of power" took place ....USSR required its part in international policy and had its geopolitical and ideological influence (USA and GB and all the West accepted that....they had to because after the WW II USSR became extremely popular). Soviet ambitions in world politics were natural....course of event seemed to confirm Communist "scientific" historiography and the thesis that history sides with USSR.
Explanation: USSR profited from Communist revolution (1917) and its role in WW II especially in 1950s. But situation started to change in 1953 (Stalin´s death and condemnation of its policy by Khruchev), in 1956 (anti-soviet uprising in Hungary) and in 1968 (Prague Spring in Czechoslovakia). Immediately after 1945 USSR was extremely popular (in Europe, in Latin America as well, Africans were inspired by Russians in their fight for independence and decolonization).