If there is one thing Iraqis want, it is to get rid of US bases on their territories. Because USA is responsible for pretty much all the current problems in Iraq. American aggression and occupation would probably cause negative effects for decades to come. Iraqis have every right to blame Americans for these problems.
So where does it say that they are secular? Seems to be a part of your claim, yet nowhere in the article you posted as your source.The only plan here is an autonomous state, not an independent one. No where in my source does it state they plan to establish a theocratic state. They'd simply be an autonomous territory just like the Iraqi Kurds and would still be part of Iraq.
On the other hand, we have a history of US supporting theocratic nutjobs in the region.