Iraq was a secular dictatorship. There were Chaldean Christians and Armenians in the government, although the vast majority were Sunni Muslims.
Saddam had a "religious awakening" after his defeat in the 1991 Gulf War [*], adding "Allahu Akbar" in Arabic script to the Iraqi flag. It was pretty transparent pandering, and Iraqi Muslims and neighboring countries didn't buy it.
[*] I've never liked the phrase "first Gulf war." The first ran from 1980-88 and was between Iran and Iraq.