You're right to worry, and Iran (heavily Shi'ite) will do all it can to give you something to worry about.
The Shi'ites are the majority -- or at least a heavy plurality -- in Iraq. If the new government is not "representative," rather than "democratic," they could democratically vote in just what you (and I) fear.
I'm sure we will be working hard to prevent that, though, and to prevent a "tyranny of the majority" in which the Kurds and Sunnis and Christians are written out of the government and oppressed as they are in Iran.
After all, we have two and a quarter centuries of working out the fine points of this very issue, and, well, we've got the guns and control of the country for now. We also have the incentive to see that the new "democratic" government isn't one that eagerly joins the "axis of evil."