There are different groups of people living in Iraq of various religions. Historically, there have been three main regions: north, south and central parts. Groups do not get along; each group wishes to have its own territory, and be distinct from the others. It makes sense for Iraq to be divided based on religions. There will not be a single state. The wars being fought in the area are largely religious wars. The radical Islam group ISIS fights its battles based on strict adherence to old Islamic laws, and allegiance to Allah. This group will not integrate with others of different religions. ISIS believes its religion is the most supreme. The quest of ISIS is to dominate, and have its religious ideologies rule the entire area. This is not realistic. As a natural outcome of war, the area will be divided based on the conquered territory of a particular religious groups, such as the Kurds or the Sunnis. They will not support each other or integrate. ISIS will probably gain its own territory eventually, and will do its own thing.
Iraq should not be divided by religion. People need to learn to live with others who may not share their word views or religion. Dividing the nation will also weaken it considerably. It will also put the non-muslim part of the nation in much danger from other neighboring muslim countries
I'm not sure that dividing up Iraq, or any country, based on religious beliefs is a great idea. There would be no way to enforce such division, and the logistics of dividing up a country based on religious beliefs would be too tremendous to try and overcome. It would serve the country better to try and find ways to live together in harmony.
The only semi-successful instance of division based entirely on religion was between India and Pakistan. Iraq will not be better off divided, it will not decrease the hostility in the region by simply splitting it. Similar to the Catholics and Protestants of Ireland, the only thing that will stop the conflicts is an internal realization of peace. The middle east is engulfed in this conflict today, but division will not solve it.