The Tang and Song rulers supported a new form of Confucianism called neo-Confucianism.
Step-by-step explanation
Confucianist ideologies were popular in China from the period of Han dynasty itself. It was developed by Confucius in 551-479 BC. The influences of Taoist and Buddhist ideologies were strong during the reign of Tang and song rulers.
The Confucian scholars then integrated the elements of Taoism and Buddhism into a single ideology which came to be known as neo-Confucianism that gained the approval of the rulers.