MEXICO CITY—On Dec. 1, tens of thousands of people gathered in Mexico City’s gritty central square to celebrate Mexican President Andrés Manuel López Obrador’s first year in office. His supporters chanted “It’s an honor to support Obrador.”

A few blocks away, thousands of protesters marched along the city’s elegant Reforma boulevard to rail against the president. Their chant was different: “It’s a horror to support Obrador.”

Since...