Something left out of that conversation (last I checked) is that Confucianism is pretty clearly not a religion by any recognizable standard, but a collection of texts, attitudes, and social practices. It is connected to religious ideas about ancestors and such, but they aren't the same. Forgot your conversation was on a tangent about Taoism, which is popularly religious.

Also creating a third term to describe the broader genre instead of slapping the Christian name on everything is probably a good call.