Supporters of the October (Tishreen) protest movement have been marking the third anniversary of a revolt that sought fundamental change in Iraq’s political order. In recent weeks, demonstrations have taken place in Baghdad and other cities making the same demand—and opposing new Prime Minister Mohammad Shia’ Al-Sudani’s government formation.

In the capital, the Popular Mobilization Units (PMU) were accused of being involved in violently dispersing supporters of the Tishreen movement in Tahrir Square. Followers of Shiite cleric and politician Muqtada Al-Sadr held their own demonstrations, following the launch in August of their self-styled “Ashura Revolution.” The latter emerged after a weeks-long Sadrist sit-in outside the parliament—and Sadr’s instruction in June that his MPs withdraw from the legislature.

The commemoration of the eruption of opposition protests in 2019 partly coincided with the parliament on Oct. 13 electing a new Iraqi president, Abdul Latif Rashid. A Kurd and a member of the Patriotic Union of Kurdistan (PUK), Rashid tasked...