Never one to revert to hysteria, I present (or rather re-present) an english translation of the draft text.
Partial Text of the Iraqi Constitution Preamble
QUOTE
We the people of Iraq, newly arisen from our disasters and looking with confidence to the future through a democratic, federal, republican system, are determined -- men and women, old and young -- to respect the rule of law, reject the policy of aggression, pay attention to women and their rights, the elderly and their cares, the children and their affairs, spread the culture of diversity and defuse terrorism.
This is the very first paragraph.
Moving on
QUOTE
Article (1): The Republic of Iraq is an independent, sovereign nation, and the system of rule in it is a democratic, federal, representative (parliamentary) republic.
Article (2): First, Islam is the official religion of the state and is a basic source of legislation:
a) No law can be passed that contradicts the undisputed rules of Islam.

No law can be passed that contradicts the principles of democracy.
c) No law can be passed that contradicts the rights and basic freedoms outlined in this constitution.
Second, this constitution guarantees the Islamic identity of the majority of the Iraqi people, and the full religious rights for all individuals, and the freedom of creed and religious practices.
QUOTE
1st -- Entities or trends that advocate, instigate, justify or propagate racism, terrorism, ''takfir'' (declaring someone an infidel), sectarian cleansing, are banned, especially the Saddamist Baath Party in Iraq and its symbols, under any name. It will be not be allowed to be part of the multilateral political system in Iraq, which should be defined according to the law.
QUOTE
Iraqis are equal before the law without discrimination because of gender, ethnicity, nationality, origin, color, religion, sect, belief, opinion or social or economic status.
QUOTE
1st -- The judiciary is independent, with no power above it other than the law.
QUOTE
Article (20): Citizens, male and female, have the right to participate in public matters and enjoy political rights, including the right to vote and run as candidates.
QUOTE
2nd -- The state is committed to protecting the individual from coercion in thought, religion or politics, and no one may be imprisoned on these bases.
The Iraqis clearly have worked to allay concerns with this document (not that the Washington Post noticed).
The idea that this creates an state anything like Iran or Saudia Arabia (the two very different from each other, by the way) is simply operating on pre-determined fears.