This controversy began in the late 16th century. At that time, Catholic Jesuit missionaries were attempting to convert the intelligentsia in China to Catholicism. In connection with this effort, the brilliant Jesuit Matteo Ricci undertook to translate the Confucian classics from Chinese into Latin, the language of scholarship in Europe at that time. As Chan Kei Thong tells us in his book Faith of Our Fathers: God in Ancient China, "During this process, Ricci discovered, to his great delight, a commonality that allowed him to present Christ to the Chinese not only in a manner that they could understand, but also in a practical way to a people who highly value pragmatism" (p. 208). Specifically, Ricci concluded that the God whom Christians worship, whom Chinese Catholic converts referred to as Tianzhu ("the Lord of Heaven"), was in fact the same God whom the ancient Chinese had worshipped, who was called Shangdi ("the Sovereign on High"). As Thong tells us, "This surprising discovery made it possible for Ricci and his associates to use established Chinese terms to express Christian ideas, to link Confucian moral concepts to Christian teachings, and to refrain from interfering with Chinese rites honoring sages and ancestors" (p. 204). However, not all of Ricci's fellow Catholics were impressed. A Franciscan missionary in China named Antonio de St. Marie argued: "What does it matter to our mission whether the ancient Chinese knew God or didn't know Him, whether they named Him in one way or another? The question is completely indifferent. We have come here to announce the Holy Gospel and not to be apostles of Confucius" (quoted in Thong, p. 205). It can be argued that in the end, the Catholic mission in China at that time was largely unsuccessful because it adopted de St. Marie's approach to converting the Chinese rather than Ricci's (although I'm not convinced that Ricci was right in thinking that traditional Chinese rites honoring Confucius and ancestors were somehow not religious in nature).
A similar controversy erupted some three centuries later when the Scottish Protestant missionary James Legge, who spent years translating many of the most important Chinese classics into English, concluded that "the Chinese had worshipped a monotheistic Deity called Shang Di, who was clearly recognizable as the Christian God" (Thong, p. 215). Other Protestant missionaries in China in the 19th century had been using the Chinese word Shen to refer to God. According to Thong: "Legge sparked a controversy with these other Western missionaries when he argued that [Shen] was equivalent to 'god' or 'spirits'" (p. 216). Legge's book The Notions of the Chinese Concerning God and Spirits "convincingly made the case that Shang Di had all along been used by the Chinese to refer exclusively to a supreme, mono-theistic God, creator and ruler of all. 'Shen,' on the other hand, he likened to the use of in English of the term 'god' with a lower case 'g' as distinguished from the word 'God' with an uppercase 'G'"...he showed that 'shen' referred to the plethora of spirits and smaller deities that populate Chinese folk religion and was not be confused with the all-powerful Shang Di" (Thong, p. 216). However, Legge was unable to convince all of his fellow Protestants, and as a result of the continuing controversy, in the early 20th century there were two versions of the Chinese Bible: "Shang Di was used in the southern edition of the Chinese Union Bible, while the northern edition used 'shen'" (Thong, p. 216). Having attended Chinese churches in the U.S. myself for a number of years, I can attest that this phenomenon can still be observed.
Whether Ricci and Legge were right in insisting that the ancient Chinese had had some knowledge of the one true God revealed in the Bible, I think it can be said that both men were very much acting in the spirit of the Apostle Paul. For example, we see Paul in his famous sermon at the Areopagus in Athens (Acts 17:16-33) quoting the Greek poets Epimenides, Aratus, and Cleanthes. Moreover, he tells his Athenian listeners: "...as I walked around and looked carefully at your objects of worship, I even found an altar with this inscription: TO AN UNKNOWN GOD. So you are ignorant of the very thing you worship--and this is what I am going to proclaim to you" (Acts 16:23). In other words, we can see that Paul attempting to connect the Gospel with the culture and beliefs of those he was seeking to evangelize, just as Ricci and Legge would do. Moreover, as I understand it, this has become a very common practice among many Christian missionaries in our own time. Of course, when taking such approach, it is always necessary to avoid the danger of syncretism--the mixing of non-Christian beliefs with Christian beliefs--but if this can be avoided, there is great potential for reducing unnecessary barriers to the Gospel.