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.
The Internet Encyclopedia of Philosophy offers all kinds of information about philosophers and their beliefs and well as specific disciplines, like Confucianism and Rationalism.