Christians under Saddam Hussein had it much better than a Christian in Saudi Arabia.
Saddam was a Sunni Arab who ruled a hostile population that was 60% Shiite Arab and 20% Kurd. He needed all the Christian allies he could get. It's also true that even Saddam was gradually Islamizing Iraq in order to appease his people. It was Saddam who added "Allahu Akbar" (Allah is the Greatest) to the Iraqi flag.
A 1991 bloody suppression of a Shi'i revolt further drove the two communities away from each other. The regime's elite was weaned of their Baathi secularism, which was replaced by Shari'ah, Qur'an and Hadith studies. Even those Baathis who remained secular at the core identified the great political advantage provided by the "Islamization" and faked Islamic piety. But which Islam? The regime's official Islam was of the soft Sunni version, but Sunni it was.Unofficially, very radical Sunni trends, anti-Shi'i Wahhabi as well as Sufi ones, were encouraged as long as they did not turn against the regime. The result was a growing sense of discrimination and oppression on the part of the Shi'ah. "Caliph" Abu Bakr al-Baghdadi, leader of ISIS/Daesh, is the result of Saddam's education, except that he performed a quantum leap in terms of radicalizing Saddam's Islam, and he abandoned Saddam's ambivalence toward the Shi'ah in favor of coherent anti-Shi'i revulsion.
Note that Iraq's population was only 20% Sunni Arab, and yet he felt the need to fall in line with the radicalism of his Sunni Arab supporters and coreligionists. It's fairly self-explanatory why the Saudi royals would fall in line with the beliefs of the 90% Wahhabist subjects. Back in the day, even the ruthless Mongols in conquered Muslim areas converted to Islam, in order to forestall rebellion among their Muslim subjects. In addition, Saddam was an enemy of ours who wanted to bring the region's oil resources under his rule, which is why he invaded Iran and then Kuwait (on his way to taking Saudi Arabia's oil fields).