Neither Taoism nor Confucianism, indeed, makes this claim.
Confucianism is an ethical rather than a religious system, and hence was able to co-exist, though not on very friendly terms, with Buddhism, which reached China about the 1st century A.D.
Confucianism is the official cult, and all officials offer sacrifices and homage at stated seasons in the Confucian temples.
Where Chinese influence had full play it introduced Confucianism, a special style in art and the Chinese system of writing.
With the relatively small Christian population and large Buddhist and Confucianism following, you may be wondering how Christmas started in China.