What he did
He performed the sacrifices and thought they mattered enormously. He declined, twice and flatly, to discuss what was at the other end of them. Asked how the spirits of the dead should be served, he said: When we cannot do our duty to the living, how can we do it to the dead? Asked about death: We know not life, how can we know death?
He believed in Heaven, and believed Heaven had a project and that he was in it. But he offered the bereaved no destination for the dead, and when the people closest to him died, his son and two of his students, he did not reach for one.
When it became a religion
In English, in the 1870s. Max Müller's series Sacred Books of the East began in 1879 and filed Confucianism as one of the world's religions, with Daoism and Buddhism to follow. Its Chinese volumes were by James Legge, the man who had translated him.
How scholars put it now
The careful formulation is Wing-tsit Chan's: religious without being a religion in the Western institutional sense. The usual diagnosis is that it is a diffused tradition, carried in families, schools and academies rather than a church, and that it is not about a god, which is the other thing the category quietly assumes.
Whether a tradition two and a half thousand years older than the category belongs inside it is a question about the category.