BAGHDAD—In a tent city under a highway overpass in Baghdad, refugees from Iraq’s Sunni province of Anbar were unanimous about whom to blame for their misery.

“I hold Americans responsible for destroying Anbar,” said former policeman Wassem Khaled, whose home was taken over by Islamic State, or ISIS, after the Iraqi army fled from Anbar’s provincial capital of Ramadi last month.

“We all know that America is providing ISIS with weapons and food, and that it is because of American backing that they have become so strong,” added Abbas Hashem, a 50-year-old who also escaped from Ramadi and now lives in the makeshift Baghdad camp that is only occasionally supplied with water.

Such conspiracy theories about America’s support for Islamic State are outlandish, no doubt. But they are so widespread that they now represent a political reality with real-world consequences—making it harder for the U.S. and allies to cobble together Iraqi forces that could regain the country’s Sunni heartland from Islamic State’s murderous rule one day.

Above all, these beliefs stem from the U.S.-led coalition’s inability to reverse Islamic State’s momentum in Iraq despite nearly 10 months of bombing. In contrast, local residents learned the hard way in past conflicts what the full force of U.S. military might looks like.