What were Chinese responses to the spread of Buddhism?

Han dynasty: No one cared much, since Confucianism was pretty strong and Buddhism wasn't about to take over anytime soon. Popular with peasants.

Period of Disorder after fall of Han: Gained a lot of popularity, especially with peasants at first, then caught on with the nobility. Some scholars converted, but not too many.

Sui: Very, very popular. It was the dominant religion (even bigger than Confucianism at the time, since the scholar-gentry hadn't made their big comeback yet) since Emperor Wen declared himself religious leader and used it to unify China for a little while.

Beginning of Tang: Still pretty popular. Buddhist scholars and monks are favored by the ruling family and Confucianism and Buddhism live in harmony.

Later Tang: Emperor Wu absolutely abhors Buddhism. Scholar-gentry makes their big comeback. Buddhism is still popular among the people, but civil service exams are in full swing and ready to put anti-Buddhists in power. Empress Wu (badass chick) is a Buddhist and favors it in her rule, but everybody else in later Tang hates it.

Hope this was helpful! :)