I think Confucianism would be best represented by a trait or something related to a government type, since there would be Muslim Confucians, Buddhist Confucians and essentially any other religion.
I agree with what you said because the majority of Chinese, whether those in history or those who now lives, do not distinguish one religion from another.
It's a common scene in China that one may find Buddha, Pagan gods and Taoism Sage in one temple and worshiped by same group of people, for they consider all deities, whether foreign one or native, holy and sacred. They hold but one belief, "I do good and God(s) will reward me."
Chinese Muslim, Christian are not among them