MEXICO CITY—Irving Pineda has received hundreds of threats since Mexican security forces arrested and then released the son of jailed drug kingpin Joaquín “El Chapo” Guzmán after an attack by cartel forces in October.

He isn’t a special-operations officer, nor a drug-cartel hitman. Rather, he’s an affable 28-year-old television reporter from local broadcaster TV Azteca who infuriated government supporters by asking President Andrés Manuel López Obrador a simple question during the president’s morning news conference a few...