In Brazil, when the country’s first female president, Dilma Rousseff, faced impeachment in 2016, following allegations of corruption and manipulation aimed at covering up the country’s financial crisis, the tabloids ran unfavorable photos of her, with her fists clenched or mouth wide open, in a concerted effort to turn public opinion against her, according to Mona Lena Krook, a professor of political science at Rutgers University. “The tabloids made it look like she was having a mental breakdown,” Dr. Krook said. “It plays into the idea that women are too emotional for politics.” Another approach paints female politicians as hyper-sexualized. That was what former President Kolinda Grabar-Kitarovic of Croatia encountered when tabloids ran pictures of another woman in a bikini and falsely claimed it was her. The photo’s subject was later identified as Coco Austin, the partner of American rapper Ice-T — but the damage to Ms. Grabar-Kitarovic’s reputation was done.