Final answer:
Confucian ideas are well-liked during stable and prosperous times as they maintain social order and support government structure, with Confucian principles especially vital for governance and aristocratic interests during the Han Dynasty and Neo-Confucianism building on moral values.
Step-by-step explanation:
Confucian ideas tend to be popular during periods of stability and prosperity because they emphasize social harmony and the proper conduct of relationships, which are key to maintaining order and ensuring a continued prosperous state. Confucianism provides a guiding philosophy that supports the role of the emperor and the structure of the government, aligns with the interests of the aristocracy, and reinforces family values. During the Han Dynasty, Confucian principles became intertwined with state governance, notably through the introduction of a Confucian-based examination system for selecting government officials. Aspiring bureaucrats were required to demonstrate mastery of Confucian texts, which tied their career success to their knowledge of Confucian teachings. Neo-Confucianism, meanwhile, integrated traditional Confucian values with a stronger emphasis on personal moral understanding, as a correction to the gentry's reliance on wealth and examinations. Despite not being the sole ideology through the ages, Confucianism consistently provided a philosophical basis that complemented periods of stability and prosperity in Chinese history.