Arraya: I would rebut the pre-1980 assertion by clarifying between terrorism in general and suicide bombings in particular.
I would say, specifically, that you’re correct about suicide bombings, pre-1980, but also that suicide bombings are something of a newer phenomenon.
There were significant spasms of terrorism and dating back to the 1960s and 1970s (think PFLP, PLO and Black September and events like Lod Airport and Munich, 1972). I’m focusing on Muslim terrorists, since that’s the topic at hand, but also remember Baader-Meinhof/Red Army Faction, Brigate Rosse, et al.
In many ways, the 1960s and 1970s were worse, in terms of violence and much of this also happened to be state-sponsored (Egypt, Syria, Jordan) or proxy (Soviets).
I guess my point would be that we’ve had extremist Muslim factions for quite a few years, but that the underlying causes have shifted from political to religious.