Historically, there has been controversy in the Church about how to see the traditional Chinese rites to honour ancestors. Here is an account from an SSPX perspective:
The unqualified welcome extended to Chinese thought and practices during the XVIIIth century was not, however, endorsed by the theologians of Europe. While the missionaries at the court of K’ang Hsi were exerting greater influence than ever before, while the number of Chinese converts reached a total of 300,000, a further aspect of Ricci’s programme had aroused bitter controversy.
Ricci had used tact and gentleness when dealing with Oriental ways of thought, realising with profound sympathy, the difficulties which faced a Chinese confronted with a strange religion. He had laid down that the mysteries of faith must be gradually unfold, otherwise irreparable shock and damage would be done to Chinese sensibility and natural pride. Afterwards, when grace had worked its miracle, the heights and depth of faith could be revealed. Moreover, after life-long study of Chinese practices he had decided that just as slavery had been tolerated in early Christian centuries until the time should be ripe for its abolition, converts might fulfill their two traditional duties, the veneration of Confucius and the dead members of their families.
As the China mission grew, Franciscans and Dominicans entered the country. Their approach to evangelisation was rather different than the Jesuits. When the Mendicants discovered that converts made by the Jesuits were allowed to honour Confucius and the tablets of the dead, they protested that a tainted form of Christianity had been introduced to China. The Mendicants forbade their converts such concessions and complained to Rome, branding Jesuits methods of adaptation as protective mimicry. Theologians of the Society rallied to the support of their missionaries. For more than seventy years the controversy raged while Rome, seeing in the problem one of the most difficult and far-reaching that had ever faced the Church, delayed her decision.
Both parties accumulated evidence. The Jesuits obtained from K’ang Hsi a written document which they believed would prove decisive. In it the Emperor stated "Honours are paid to Confucius, not as a petition for favours, intelligence or high office but as to a Master, because of the magnificent moral teaching which he has left to posterity. As for the ceremony in honour of dead ancestors, it originates in the desire to show filial piety. This ceremony contains no request for help. It is practiced only to show filial respect to the dead. Souls of ancestors are not held to reside in the tablets; these are only symbols which serve to express gratitude and keep the dead in memory, as though they were actually present."
On their side, the Mendicants maintained that, despite all appeals to authority and tradition, in actual fact such honours as practiced by the majority of Chinese, were tainted with superstition. Confucius they protested, was venerated not merely as a teacher, but as the highest of saints, a superhuman being, while most Chinese held that the souls of their ancestors were actually present in the tablets and feasted on the food offered to them.
It must be said that while they opposed themselves so vividly, not one of the missionaries ever thought to establish a kind of syncretism between the pagan religions and Christianity, such, unfortunately, as is being done after Vatican II, in the name of ecumenism. However there were some practices not specifically religious which need to be studied in reference to the value given to them concretely in the society which practices them.
Missionaries were divided in the question of rites and beyond these in the difference of approaches: the tabula rasa (clean slate) method or the method of a certain adaptation. Such a controversy could not be solved at the mission. Rome at to intervene. She did so the Roman way i.e. slowly and prudently. Pope Benedict XIV (1741 - 1758) ended the dispute in two documents of 1742 and 1744, maintaining previous censures and reminding missionaries that their role was less to adapt at all cost than to convert. In order for the situation to be totally clarified, it took a lot of time, the time for the popular mind to desacralize all of these rites. This is precisely what was declared in the pontifical instruction of December 8, 1939.
Obviously taking either side of this debate is reasonable or it would not have been such a matter of controversy. The earlier Church decrees forbade Catholics from participating in rituals of ancestor worship and deemed them heathen superstition. The instruction of 1939 treated them as secular customs that were permissible for Catholics.