President Trump’s decision to join the region-wide pushback against Iran and its allied militias reminds me of the movie Casablanca. That’s the World War II drama in which Humphrey Bogart’s cynical saloon keeper, Rick Blaine, an ex-gun-runner, gives his coveted letter of transit to the resistance hero Victor Laszlo, who tells Rick: “Welcome back to the fight. This time I know our side will win.”

Blaine, the cynical Casablanca saloon owner, turned out to have been on the good guys’ side all along. Not so America in Iraq. Fighting ISIS as our baddest regional enemy, the Obama administration allied with and armed the same Iranian-backed militias that a decade earlier had exacted the highest GI casualties.

Mr. Trump has seemed to be on the fence, squeezing Iran financially, while hanging back militarily — closer to Blaine’s “I stick my neck out for nobody.” While he declared a desire to end “endless wars,” Iran and its proxies grew ever bolder, hitting oil tankers in the Gulf, bombing a Saudi pipeline, orchestrating suicide attacks in Afghanistan and partially disabling Aramco’s oil fields. Mr. Trump dismissed Pentagon plans for a pushback even after an America drone was downed by Iran.

On Friday, though, the largest Iraqi Shiite militia, Ktaib Hezbollah, killed an American contractor and wounded four soldiers. An American airstrike against the Iranian proxy killed at least 25 of its fighters. As New Year’s Eve neared, the militia, surrounded by loyal recruits, entered Baghdad’s green zone and surrounded our embassy, shouting anti-American slogans, while security forces used tea gas to disperse the crowd.

Critics caviled. Brookings’ Michael O’Hanlon worried on Fox News that America would lose its ability to influence Baghdad politics. Indeed, Prime Minister Adel Abdul Mahdi’s office on Monday condemned America’s “unacceptable vicious assault that will have dangerous consequences.”

No surprise there. Mr. Mahdi, like several of his predecessors, is under Iran’s thumb. Which is where the new fight must start. Iraqis, including Shiites, have been out in the streets, demonstrating against Iran’s influence for months. Iran and its allies have viciously killed dozens of citizens protesting the corruption, violence, and paralysis dominating their Tehran-dominated political class.

On Tuesday, anti-American protesters lauded “our leader Soleimani” — a reference to Iran’s al-Quds commander, General Qassem Soleimani, who’s charged with exporting Iran’s revolution in the region and beyond. The wily strategist has long organized militias modeled after Lebanon’s Hezbollah in Yemen, Syria, Afghanistan, and elsewhere — traveling the world even as he was under a UN-mandated travel ban.

General Soleimani’s top ally in Iraq is his personal friend Abu Mahdi al Muhandis, “the engineer,” who leads Ktaib Hezbollah, which is by far the country’s largest armed militia. Created by General Soleimani in 2007, it now boasts 30,000 fighters, according to Jonathan Spyer of the Jerusalem Institute for Strategy and Security and the Middle East Forum. He was embedded with the group in 2015.

At the height of Mr. Obama’s war against ISIS, Ktaib Hezbollah was America’s top ally in Iraq. No wonder veterans of the previous administration now boast there were no attacks on Americans during that time: they allowed Iraq to slip further into its powerful eastern neighbor’s orbit, literally buying Iran’s alliance.

It was a good arrangement all around, except, as the nation-wide protests show, it didn’t work well for Iraqis. Always leery of Persians seeking to dominate them, the country’s Arab majorities called out their government. Last month, in a highly symbolic event, Iraqi Shiite demonstrators marched on the sect’s holy city of Karbala, denouncing the Baghdad government as an “Iranian puppet.”

America has made many mistakes since launching the 2003 Iraq War. But appealing to the country’s popular anti-Iran sentiment shouldn’t be one of them. Such sentiments are prevalent beyond Iraq, in Lebanon, Yemen, Syria, and Iran itself. General Soleimani was riding high for too long, directly aided at times by America and banking on our desire to end all Mideast involvement.

Mr. Trump has changed the equation by leaving the Iran nuclear pact and slapping Tehran with sanctions that helped the region’s pushback against Soleimani & Co. Sunday’s action could signal the addition of a military dimension to America’s effort at ending Tehran’s bid to be the region’s top player.

It won’t be easy. Israel has been fighting for years against General Soleimani and his minions in Syria, Lebanon, and, recently, Iraq. The IDF, though, has so far merely managed to mow the lawn. America could tip the scales and change the nature of the fight.

John Bolton, a former National Security adviser, has tweeted that Sunday’s attack was “overdue, but a good first step.” Many Mideasterners pray for a significant followup.

Twitter @bennyavni