Did the Soviets infiltrate the American anti-nuclear movement in the 80s?

This was a perennial accusation by the anti-anti-nuclear folks in the 1980s (i.e., anti-Communist, pro-Reagan, pro-nuke). I've never seen any evidence of significant "infiltration" offered; at best, right-wing scholars find a retired Soviet intelligence agent who will say "yes, it was all a scam!" but these sorts of statements are problematic in and of themselves (for reasons that are fairly obvious).

In all political movements there are individuals who are variously influential to different policies, and there were certainly members of the anti-nuclear movement who were socialists. That some of their positions might have benefited the Soviet Union in some way doesn't mean they were Soviet agents, though — at worst, they could be considered "useful idiots" (to use a Cold War term), people who might not be actually working for the USSR but whose policies were useful to them (and they might interpret the USSR in a very favorable way as well).

I hesitate to call these sorts of things "conspiracy theories" because they generally aren't very elaborate, and lack the attempts at evidence that usually mark real "conspiracy theorists." So for example when Sagan et al. published their work on the idea of "nuclear winter" there were many then, and still some today, who allege that the whole thing was a Soviet creation meant to encourage a weaker US foreign posture. There is no actual evidence of serious influence. The Soviets did support some aspects of the US scientists' discussions about nuclear winter, and did attempt to collaborate in a weak way, but that does not denigrate from the work of the US scientists (even if the Soviets had been doing it cynically, which isn't clear). The Soviet contributions were noted, but they were also criticized for any deficits they might have. If you go over the history in depth I don't think there can be any doubt about the sincerity and independence of the US researchers (even if one doubts their conclusions, models, etc.). Any notion that the data was somehow "faked by the KGB" neglects any understanding of how these peer-reviewed scientific articles were developed, vetted, and discussed at length over many years of research (some of which still continues to this day). Did these scientists think their work had political implications? Obviously and explicitly. But that doesn't mean it's wrong or tainted, much less a foreign "fake." (On this, see Lawrence Badash, A Nuclear Winter's Tale, which is sort of the definitive history of nuclear winter theories and research.)

The Soviets did funnel money into groups (through front organizations) that it considered in its interests. As did the CIA, conversely, and probably many other intelligence groups internationally. Often groups that received such funds had no idea who they were actually receiving it from — they were being "used" only in the sense that their existence was useful, not so much that they had orders dictated to them from abroad. (On this, see Frances Saunders, The Cultural Cold War.)

In any case, while there is value in knowing who is funding what, and what interests a nation might have in a policy, all of these efforts are moves to avoid actually engaging with the issues under discussion. That is, if you can wave your hand and say, "ah, the Soviets were behind the nuclear freeze movement," it means you don't have to engage with those beliefs as legitimate ones. Even if it were true that there was significant Soviet influence in those movements (which, again, I have not seen real evidence of, and I doubt), that doesn't explain why they were popular with so many people, and it doesn't mean the ideas they espoused were actually bad ones. Similarly, just because the US government and its industrial interests supported or opposed some idea doesn't make it immediately tainted, either.

Civil rights is a good example of this: did the USSR try to influence the push for full rights for African-Americans in the 1930s through 1960s? Yes. Did they do it cynically (in that they pushed for it because they thought it would benefit them, not African-Americans)? Yes. Does that mean that everyone in favor of civil rights was a Soviet agent? Obviously not. Does it mean that civil rights as an idea and movement was irrevocably tainted by association? No.