First of all, it's fairly damning of the morality of those making that claim since they apparently felt fine with a genocidal dictator as long as Saddam resisted Iran.
Second, are those people making that argument admitting that Iran under the mullahs needs to be opposed? Huh. Fancy that. But I digress.
Most importantly, the argument we turned Iraq into an Iranian puppet is hogwash. If Iraq is now run by people naturally friendly to Iran, why would Iran expend so much effort killing Iraqis by supporting both Sadrist death squads and backing Sunni jihadis both directly and indirectly by supporting Syria who sent in suicide bombers to plague Iraq?
And why, if Iraq is such a pliant Iranian ally, would Iran bother to rattle their sabre against Iraq over a disputed oil field? Strategypage writes of that incident:
The Iraqi government is still trying to figure out what Iran was trying to accomplish by recently moving a few troops into a tiny piece of Iraqi territory in the south. Iran believes the current border should be farther west, and Iraq was told that there were no Iranian troops in Iraq. The Iraqi government eventually sent the army and police to ask the Iranian troops to withdraw. Meanwhile, the incident they caused widespread anti-Iranian demonstrations in Iraq. [emphasis added]
Working up some good anger against the Persians isn't that tough for Iraqis of all backgrounds. Don't forget that Iraq's Shias willingly fought and died in large numbers to resist "fellow" Shias in Iran during the 1980s First Gulf War (Iran-Iraq War).
Iraq is an increasingly powerful American ally and not a puppet of Iran. I dare say that Iraq will not have stronger relations with some of our enemies than a lot of our NATO allies have.