Possibly for reasons similar to why Medieval nobles would put Jews into many court positions: you don't want to hand power over to anybody who could have ambitions for the top job. A Christian COULD NOT become ruler of a Muslim country, so they would not be a worry to Saddam
Tarik Aziz, Saddam's foreign minister, is a Christian in a top job. I think what we all overlooked was that Saddam was a SECULAR dictator who modelled himself on Stalin. This may start a fecal tsunami, but the Osama-Saddam links never were credible to me for that reason. Many countries have had similar dictators -- who focused on modernization at the expense of ethnic and religious loyalties -- who are today seen as unfortunate, but necessary, players in their country's history: Ataturk in Turkey, Porfirio Diaz in Mexico, Stalin, etc.
I'm sorry to say it looks as if we went into this war without even looking up Iraq in an encyclopedia.