This is only a very quick writeup on the Palestinian groups, as I don't have a lot of time (it's late here and work starts entirely too soon), so I invite everyone to expand on this and/or provide a whole new answer.

How important was Islam for Palestinian groups in the 70s? Not overly important. It was, if at all, mostly used for propaganda reasons.

During the seventies, the main Palestinian terrorist organization was the Fatah, the leading party and main body of the Palestinian Liberation Organization, the PLO. The Fatah took over political leadership from the pan-arabic Baath party after the Six-Days-War and have shaped the political nature of the Palestinian underground movement ever since until their emergence as the main political body of the Palestinian Authority (PA). The Fatah itself was strictly secular, as were most other groups within the PLO in the timeframe you asked about.

It wasn't until the first intifada in 1987 that Islam became a driving force in the Palestinian underground movement. The Hamas became powerful during the intifada and Fatah saw themselves forced to found their own "Islamic" group, the Al-Aqsa Martyr Brigades (even though their Islamism is highly debatable since the Fatah doesn't want Islamists to gain significant power within their organization).

When the Oslo Accord rolled around in 1994 and the PA was established, the Fatah had to give up their underground activities in an effort to become the official political representatives of the Palestinians. This left a huge void that coincided with a rising Islamist tendency in the Arab world and was subsequently filled by various Islamist groups. The failure of the PA to end the perceived Israeli occupation of Palestinian land only fueled their success - the secular road was apparently the second one to fail the Palestinians after the Pan-Arabic movement. So now many people turned their hope to Islam and Islamic groups.

So, in conclusion: Islam only played a nominal factor in the 1970s and didn't become a significant factor in Palestinian politics until the first intifada and the early 1990s.

Sources (only two since this was only a very quick write up):

Abusada, Mkhaimar: "Islam versus Secularism in Palestine: Hamas vs. Fatah", Conference Paper for the "The Transformation of Palestine: Palestine and the Palestinians 60 Years after the ‘Nakba’" Conference, Heinrich Böll Stiftung, Berlin, March, 2010

Sayigh, Yezid: "Struggle Within, Struggle Without: the Transformation of PLO politics since 1982,", in: International Affairs vol. 65, no. 2 (spring 1989), p. 247–271