I agree with my friend John Enright that there are perhaps two senses/types of 'Confucianism', one philosophical and the other religious (though not in an overtly otherworldly manner); the same is true of Taoism and Buddhism in Chinese thought. This duality is well captured by the ambiguity in meaning of the term that is often translated "heaven", namely the Chinese word T'ien: this word can just as well be translated "nature", and often is. This ambiguity may well relate to the fact that there is no strong distinction or dichotomy in Chinese thought (and perhaps Indian, though I am not as familiar with that tradition) between philosophy and religion or reason and faith -- or, for that matter, between mind and body, reason and emotion, man and nature, truth and goodness, politics and morality, knowledge and action, or the secular and the sacred. There are good and bad aspects to this kind of integrated perspective, but I know I've found a lot of value in it since it is so opposed to much of western thought (and in line with some of Rand's thinking, it seems to me). My main point is that Chinese philosophy has a strong naturalistic streak, which I find to be a refreshing change from the Christian tradition. If one must have religion, I'd rather it be a naturalistic one!
But of course, as Fung Yu-Lan says, it isn't necessary that one have religion:
It is not necessary that man should be religious, but it is necessary that he should be philosophical. When he is philosophical, he has the very best of the blessings of religion.