Politically, Nationalist China's Chiang Kaishek must be considered a "strange bedfellow with Cai Yuanpei. Chiang was a disciplined, narrow-minded conservative of the type one might expect from a military man. Cai, a one-time Chancellor of the University of Beijing, was a self-proclaimed revolutionary and a "freethinker" who might be characterized as "progressive," or even "pinko," by American political analysts. More to the point, he recruited and nutured future Communist leaders such as Chen Duxiu, Li Dazhou and Zhou Enlai at the University of Beijing.
Yet, within the divided Nationalist party, Cai was a man that tipped the balance in favor of Chiang Kaishek, by leading the movement to purge Communists (led by Cai's former students) from the Nationalist Party. In 1928, when Chiang set up his Nationalist government, Cai was made President of the Control Yuan (roughly Auditor General), a position created just for him.
As the American son of Chinese immigrant parents, I know that is far more likely in China than in the western world for two people of diametrically opposing ideologies to be allies because of family ties, friendship, or other relationships, a situation known as "guanxi" (which means "connections" or "relationships.") Given the improbability of this co-operation, does anyone know what family or other connection might have bound Chiang and Cai? (My parents were unable to answer this question.)
Hint: One of the the sisters of Madame Chiang Kaishek (that is, Chiang's sister in law) was a Communist aka Madame Sun Yatsen. Could Cai Yuanpei have had a connection to this sister? Something like this could explain Chiang's co-operation with some as far left as Cai.