During the thirteenth and fourteenth centuries, the Chinese people were primarily seeking freedom from Mongol rule. This period marked the time of the Yuan Dynasty (1271-1368), established by Kublai Khan, a Mongol leader. The Mongols ruled China for nearly a century, and many Han Chinese experienced significant cultural and economic suppression under their dominance, leading to various uprisings and a desire for autonomy and self-governance.
While there were instances of religious persecution, the primary struggle during this period was against the Mongol rulers and their policies, which often marginalized the native Chinese population. Therefore, the most accurate response regarding what the Chinese people were seeking freedom from during the thirteenth and fourteenth centuries is Mongol rule.