Here you can find answers to the previously asked similar question:

/u/The_Alaskan and deleted account in What was going on in 1985 that would have made Libya the go-to reference for Doc Brown's illicit plutonium sourcing in Back To The Future?

Separate from the specificity of Libya (they could have used any number of different groups, if they wanted to), the fear of terrorist acquisition of nuclear weapons, specifically Middle Eastern terrorists, became a major issue in the 1970s. Fears of nuclear terrorism in general became a wide trope in the early 1970s (spurred on largely by the activism of Los Alamos weapons designs Ted Taylor, whose fears were heavily publicized in John McPhee's The Curve of Binding Energy, as well as through stunts like John Aristotle Phillips turning in a nuclear weapon design as a junior thesis project at Princeton). After the Munich massacre at the 1972 Olympics, in which Palestinian terrorists orchestrated a complex plan to kill Israeli athletes, fears of specifically Middle Eastern terrorism became a major part of the Western milieu, and joined with fears of nuclear terrorism. So all of the parts are in place for "Libyan terrorists who want plutonium" to be a totally recognizable trope in 1985. They could have also changed "Libyan" to a variety of other places and have it still work — "Palestinian" and "East German" come to mind as recognizable "terrorist threats" for that time (whereas militant left-wing American terrorist groups, like the Weatherman, had faded out of relevancy, and the Japanese terror cult Aum Shinrikyo had not yet entered into it; for 1985, a reference to the Rajneesh might have glossed in a way that it would not today), whereas "Pakistani" would be less about a terrorist acquisition and more about a state one (the Pakistanis attempted to buy Phillips' thesis off of him, amazingly).

Late to the topic, I'm afraid, but this is certainly an area that falls within my research interests! In fact, my latest published article (in Diplomatic History) mentions Back to the Future in passing! From 1979 onwards, there developed a trope/conspiracy theory around the so-called 'Islamic bomb'. In short, this was the notion that if one 'Muslim' state (generally Pakistan) gained access to nuclear capability, then that capability would be shared around other 'Muslim' states because of the bonds of faith. The 'Islamic bomb' actually stemmed from rhetorical devices used by Pakistani leaders Zulfikar Ali Bhutto and Muhammad Zia ul-Haq, but entered 'Western' discourse on nuclear weapons after the twin shocks of the Iranian revolution and the early 1979 revelations about A Q Khan's 1975 theft of centrifuge designs from the Almelo plant in the Netherlands. These two separate events melded Islamic radicalism and nuclear weapons in the minds of observers. Given Libya's claimed desire for nuclear capability, previous relationship with Pakistan (that had deteriorated dramatically after Zia came to power), and perceived (and actual) radicalism, it was no surprise that they popped up in BTTF. If you'd like to know more, I'll actually be talking about this in the upcoming Ask Historians digital conference!

Cheers,

Malcolm