In the 1960s, there were a lot of third-world resistance movements whose members were either Muslim or from Muslim backgrounds, but they tended to channel their greivances through left-wing movements, rather than religious ones.
There were Muslim terrorist organizations in the 1970s-80s.
Here in the Philippines, the Moro National Liberation Front was established in 1972. The cause of establishment was growing discontent with Ferdinand Marcos and the Jabidah Masacre in 1968. During the 1970s, the group attempted to have the island of Mindanao secede from the Republic. This culminated it an all out war in the 1970s which saw the bloodiest battle the AFP had since WWII. The city of Jolo was destroyed in an intense bombing, naval bombardment, and urban warfare.
Sadly can't find videos of it in English, but I did find this AP Archive from 1975:
The PLO is one of them. It's the reason why Israel invaded Lebanon in 1982.
The bombing of the U.S. Marine barracks in Lebanon in 1983 was suspected to be committed by Hezbollah under the name Islamic Jihad Organization. Admittedly, this is the first time I heard the word "jihad" used in terrorism, correct me if I'm wrong.