Final answer:
Buddhism influenced Zhu Xi and Neo-Confucianism by challenging Confucian ideals, leading to a revival and reinterpretation of Confucianism that emphasized rationality, moral understanding, and personal effort. Neo-Confucianism incorporated a critique of Buddhism and promoted ethical social mobility.
Step-by-step explanation:
Buddhism significantly influenced Zhu Xi and the development of Neo-Confucianism. The rise of Buddhism and Daoism in Chinese culture challenged traditional Confucian ideals, spurring Neo-Confucians like Zhu Xi to respond. Buddhism provided a path outside familial structures through monkhood and nunnery, and its doctrines contributed to the commercialization and public roles in society. Therefore, Neo-Confucians, in an effort to revive Confucian thought, incorporated a critical engagement with Buddhism while reinforcing the importance of moral understanding and personal effort from Confucianism.
Additionally, Buddhists practices such as charity became influential, and the economic practices associated with Buddhism, such as loans and joint-stock companies, impacted the social structure. Zhu Xi aimed to expunge the impact of Buddhism by promoting classical prose and traditional teachings of Confucius, emphasizing rationality and ethical conduct.
The integration and interpretation of Buddhist concepts within Neo-Confucianism under Zhu Xi and others helped establish a more humanistic approach to Confucian philosophy, offering ethical social mobility and giving rise to a strand of Confucianism that stood out during the Song dynasty and was later accepted as state orthodoxy under the Yuan dynasty.