During which period did the united states and nato allies view the soviet union as the prime exporter and sponsor of modern-day terrorism?

This era would be known as the Cold War period. This period of time is when the US and Soviet Union faced off in a battle of political power and global influence. The US (in support of capitalism) and the Soviet Union (in favor of communism) constantly tried to limit the power of each other. In order to show their political power, each country made allies.

NATO (North Atlantic Treaty Organization) was a political and military alliance between countries like the US, Great Britain, France, Denmark, Italy, and Canada which focused on stopping the spread of communism. These countries were worried that nations influenced by the Soviet Union would turn into one similar to the Soviet regime. These countries did not like this communist regime, as the rights and individual liberties of the citizens were severely limited.