I think there’s two ways to cut this quote depending on what we want to emphasize. Emphasize the examples:

During the Cold War, the anticommunist ideological framework could transform any data about existing communist societies into hostile evidence. If the Soviets refused to negotiate a point, they were intransigent and belligerent; if they appeared willing to make concessions, this was but a skillful ploy to put us off our guard. By opposing arms limitations, they would have demonstrated their aggressive intent; but when in fact they supported most armament treaties, it was because they were mendacious and manipulative. If the churches in the USSR were empty, this demonstrated that religion was suppressed; but if the churches were full, this meant the people were rejecting the regime’s atheistic ideology

Or emphasize the conclusion:

In the United States, for over a hundred years, the ruling interests tirelessly propagated anticommunism among the populace, until it became more like a religious orthodoxy than a political analysis. During the Cold War, the anticommunist ideological framework could transform any data about existing communist societies into hostile evidence. If the Soviets refused to negotiate a point, they were intransigent and belligerent; […] If communists in the United States played an important role struggling for the rights of workers, the poor, African-Americans, women, and others, this was only their guileful way of gathering support among disfranchised groups and gaining power for themselves. How one gained power by fighting for the rights of powerless groups was never explained. What we are dealing with is a nonfalsifiable orthodoxy, so assiduously marketed by the ruling interests that it affected people across the entire political spectrum.

There’s probably even more ways to narrate it.