Ms. Takaichi, 64, is a divisive figure in Japan, and her breaking of the glass ceiling has drawn a range of reactions. Her supporters have hailed her as a pioneer who knows firsthand the challenges of Japan’s male-dominated culture. Activists and scholars have expressed concern that she will continue to support policies that have held Japanese women back. Political rivals have accused her of serving as a puppet to men in her party; one male lawmaker recently described her as a bride who had married into a powerful political faction.