Looking for ways that the New Culture Movement was associated with Chinese Communism or the Chinese Communist Party.
The New Culture Movement was an intellectual revolution in China during the early 20th century. In a large sense it marked the birth of Communism in China.
Originally, the movement emerged as a reaction to Chinese diplomatic weakness by the traditional literati. The movement was championed by intellectuals who had grown disillusioned with the early republican government, beginning in 1915 with the Chinese capitulation to Japan's Twenty-One Demands. Leading proponents of the movement include Hu Shih, Chien Hsüantung, Chen Tuhsiu, and Lu Hsün. Of these characters, Chen was a Trotskyist who co-founded the Chinese Communist Party, while Lu Hsün was a leftist who was sympathetic to Communism. Many involved were educators in the great universities.
Within a few years discontent at foreign imperialism reached new heights over the Shantung Problem at Versailles. This culminated in the May Fourth Movement of 1919, emerging as a product of student (and professorial) activism in the great universities. A number of its leading members went on to become high ranking members of the Chinese Communist party, including co-founder Teng Chung-hsia and future first premier of the People's Republic, Zhou Enlai.
The nature of both movements were to reject Chinese traditionalism, and import new Western ideas. This includes Communism, which were taken up by several leading members as mentioned above. Due to their influence, the May Fourth Movement became an early conduit for Communism to be introduced to the masses. The Chinese Communist Party was founded shortly after in 1921.
Anniversaries of the May Fourth Movement continues to be celebrated in Communist China.
According to Wikipedia,
"The founders of the New Culture Movement clustered in Peking University, where they were recruited by Cai Yuanpei when he became chancellor. Chen Duxiu as dean and Li Dazhao as librarian."
All three of them were "progressive" in their thinking. After they moved just a bit further left "the Chinese Communist Party was founded in 1921, chiefly by Chen Duxiu and Li Dazhao." On the other hand, Cai Yuan Pei tilted "right" (compared to the other two), and became a "purger" of Communists, including his two former proteges, by supporting Chiang Kai Shek.