And? During the time you reference, China was a kind of feudal state, run--to the extent it was run at all--by competing warlords. All of the developed nations had a stake there. As what you wrote points out, there was also an active interest on the part of westerners to convert Chinese people to Christianity.
Those efforts were quite successful. Many of the Christian Chinese became professionals--doctors and teachers--and others became businessmen, industrialists, or politicians. Soong Mei-Ling--better known as Madame Chiang Kai-shek, was educated in the States, along with her sisters. She married Generalissimo Chiang Kai-she, one of the most successful warlords, and was very well-known here.
In the years before WWII, Japan invaded China and occupied Manchuria. The occupation was exceptionally cruel. Once WWII began, the US and European nations, including the Soviet Union, much of which bordered on China, tried to help. But things were changing. In the late '30s, the troops of China Kai-Shek's rival Mao Zedong drove the French out of Shanghai. The warlords more or less united to fight the Japanese, but once Japan was defeated, a civil war broke out in earnest. It ended with Mao's victory in 1949.
Everyone was "obsessed with China". I fail to see why you'd single out the Rockefellers.
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