This is more about history than English.
Without getting into a history lesson, during the Cold War, when tensions were highest between the capitalist USA and the communist USSR, there was great fear in of enemy subversives in both camps. As a consequence, it was dangerous to be a communist in the United States¹.
This got particularly bad during the 1950s, as a result of fear mongering by Senator Joseph McCarthy, during what was known as the (second) "Red Scare" ("Red" here being a metonym for communists, their adopted color). From Britannica:
The term McCarthyism is applied to the persecution of innocent people using powerful but unproved allegations. It refers to U.S. Senator Joseph McCarthy's charges of communist subversion and high treason in the U.S. federal government in 1950s.
In brief, ostensibly in pursuit of ferreting out Soviet agents and subversives, McCarthy and people in his sphere of influence started lobbing accusations of being a secret communist at all political enemies, indiscriminately, on the flimsiest evidence, or sometimes none at all, and even worse, sometimes fabricated.
These smear campaigns ended careers and sometimes lives, and are a dark stain on American history; so much so that the period is sometimes likened to an earlier dark era, characterized by false accusations and persecution: a "witch hunt"².
So Paul's implication to Julia in saying:
Paul: We haven't done anything. That's not the point. The point is, we were in China. And that's practically sufficient.
Is that they have been to China. Communist China. And under McCarthyism, that's enough to be condemned ("If you're not communists, why did you visit communist China? Admit it, pinko!").
¹ Not quite as dangerous as being a capitalist in the USSR, if the tales of late night visits by the KGB are to be believed. Or, as the Yakov Smirnov joke went:
In United States, you can criticize government. Yes. Also, in Soviet Russia, you can criticize government. Once.
² You can read more in the Wikipedia article on McCarthyism.