Iraq has always had deep rooted tribes and sects. Enough of them to cause instability in the country. Sadam squashed that because he ruled with an iron fist and instilled fear into the population. That is not the same thing as being a secular country.
That is not to say that there are no secularists in Iraq. It is to say there aren’t nearly enough to counter those that engage in tribal and sectarian fighting and yes Islam is either at the root of that or is used by those mullahs in power in order to control people.
I am pessimistic of the long term stability of Iraq after we leave unless there is a central govt in Iraq that can put down insurgencies and that is hard to do without resorting to the type of brutality our military can never get away with again within the liberal world opinion that our foreign policy makers allow themselves to be manipulated by and therefore restrain our military with.