Iraq under Baath Party rule, had a nominally secularish government. The central tenet of the Baath party ideology was that of Arab national unity, and despite the eventual failure of the effort, the political unification of Arab lands under one government was their goal.

Notably, the party was originally founded by a Christian, Michel Aflaq. The party wasn't entirely secular, as many of its members saw Islam as central to Arab nationalism at least on a cultural level. It was formally non-sectarian. The Sunni-Shia divide was one that they wished to mend through the elevation of a shared Arab national identity over religious identities.

Saddam Hussein had been a player in the Baath Party for many years before he took power in Iraq, and was, or at least appeared to be, a supporter of Michel Aflaq's wing of the party. I think it is hard to read Saddam, and so I could only speculate on where he really stood in terms of how much he really believed in the Baath party's ideology and how much it served only as a pathway to power and influence for him. I think the truth is somewhere in the middle, and that Saddam was strongly seduced by power once it was within his reach and finally in his hands.

Ahmed Hassan al-Bakr, who preceded Saddam as President, relied heavily on nepotism and cronyism to build himself a loyal base of support within the party to insulate his authority from the factional infighting, both as President and also as a Baath Party leader before taking power in the 1966 Coup. This nepotism and cronyism led to over-representation of Sunni's from Tikrit in positions of power. Saddam was always powerful in the al-Bakr government and was the de-facto leader of the government years before he actually ascended to the presidency. He too continued the nepotism and cronyism and relied on familial and tribal relations to protect his power with loyalty. So while the government was nominally non-sectarian, one sect was over-represented in government.