At the time, Irak was actually far from playing the religious card, knowing that Husein was a sunni but the shiite community was larger if you don't include the kurds (who Husein butchered as they were hostile to him). Now, it's between Saoudis, Qataris and Iran.
History lessons are a long time ago for me... Wasn't there a fear that the revolution in Iran would spark Shia unrest within Iraq?
 Checked wikipedia: that was it. The rest of the dynamics escapes me, and I don't feel like reading all of it. Reading another book right now.