Not sure this would fall into the realm of 'science fiction', but I think the film "The Day After" (1983 - TV movie about the aftermath of a nuclear war) merits a mention. Wikipedia says why better than I can:
"President Ronald Reagan watched the film several days before its screening, on 5 November 1983. He wrote in his diary that the film was "very effective and left me greatly depressed," and that it changed his mind on the prevailing policy on a "nuclear war". The film was also screened for the Joint Chiefs of Staff. A government advisor who attended the screening, a friend of Meyer's, told him "If you wanted to draw blood, you did it. Those guys sat there like they were turned to stone." Three years later, the Intermediate-Range Nuclear Forces Treaty was signed at Reykjavik, and in Reagan's memoirs he drew a direct line from the film to the signing. Indeed, an oft-repeated story was that Reagan sent Meyer a telegram after the summit, saying, 'Don't think your movie didn't have any part of this, because it did.' In a 2010 interview Meyer said that this was a myth, and that the sentiment stemmed from a friend's letter to Meyer; he suggested the story had origins in editing notes received from the White House during the production, which "may have been a joke, but it wouldn't surprise me, him being an old Hollywood guy". The film also had impact outside the US. In 1987 during the era of Mikhail Gorbachev's glasnost and perestroika reforms, the film was shown on Soviet television.