No there were broader geopolitical considerations than Kuwaiti and Saudi royal families. We overthrew Saddam because he was a brutal thug. Granted he was our thug and he did have support Christians under his rule. The problem is that there are no good solutions in the Middle East, either you have authoritarian allies like the Saudis or fundamentalists like Iran. Or alternatively, Assad, Saddam, etc. Or anarchy (ISIS).
If an American government was hell-bent on eradicating Christianity from the Middle East, it couldn't implement a more effective course of action than what was done under those two Bush @ssholes.
What would you have done instead?
I would have armed Saddam Hussein back in 1990 and let him invade Kuwait and Iraq.