MEXICO CITY—Andres Manuel Lopez Obrador was officially sworn in as Mexico’s new president on Dec. 1, but for many Mexicans, it seemed as if he had already taken office months ago, eager to shake things up. Near-daily press conferences on the steps of his Mexico City apartment building, promises of informal popular referendums on any number of policy issues, and a notably antagonistic stance toward both opposition forces and the media suggest a new era of uncertainty for Mexico.

The veteran leftist, better known in Mexico by his initials “AMLO,” rode to a landslide victory in July’s election, vowing to stamp out corruption, tame drug violence and reduce economic inequality. His openly populist tendencies may signal a major watershed in the way Mexico, which earned a reputation for democratic stability and a newfound openness to markets in recent years, is governed. ...