Yeah, I can tell you now that religion does not come up much within Kingdom. Only recently, as in the last few chapters, has anything remotely involving it came up, and that was mostly about how the King Ei Sei believed that a united China should be ruled. Which was under a legalistic perspective where all were equal under the law and that even the conquered would be treated no differently than the conquering Qin. Though he also seems to reference Confucianism when he states that humanity is light in his argument with Ryofui, so I am unsure of what that says about his religious beliefs.
Your piety option is not mutually exclusive, you are not becoming a disciple of the religion you are learning about. You can eventually study all four if you want to. Right now you are simply choosing a philosophy which you believe would benefit you to learn. You might be able to later dedicate yourself to one of these philosophies, or even form your own if you have a high enough piety, but that time is not now.
Also, in regards to Taoism and Confucianism. Keep in mind that both of them are in their early stages so what you know of them now will not be what they are currently in the quest. For example, Taoism is very different from how it is today in that it hasn't formed an organized religion yet and only two of its important texts have been written, the Tao Te Ching and the I Ching.
Helping to clarify(being raised as nominally a Taoist).
Chinese religion is a pretty big blend:
-Confuscianism is the cultural moral code. It lays no claims to the supernatural, only that this is the basic nature of humanity, and that we should nurture it. Nearly everyone follows it to some extent, though, as someone blatantly in violation(kinslaying, treason or rebellion) are simply not honorable to associate with.
--Ancestor worship is tied to it for obvious reasons of filial piety, it's very important to keep track of and paying respects to all your forebears, and to make sure that your descendants keep the torch going.
-Legalism/Mohism is something closer to the code of chivalry or the Hippocratic Oath. It's something only really held by scholars and nobility(aka the people who advise the laws and set the laws). It's promoted for the purpose of bringing order to a chaotic world, as an entirely practical element. Both schools lay claim to "this is how we fix the world".
-Taoism is the belief in the natural and supernatural world, how to influence it, and how to deal with it influencing you. It contains much of the foundations of chinese astronomy, weather forecasting, chemistry, metallurgy, herbology, architecture etc.
--This early in the timeline, it had not yet picked up a lot of the later animistic baggage and deification, but while the philosophy itself is only really dedicated to by academics and the elite, the practical gains of someone making a study of things like
predicting when floods happen and things of everyday value like building your homes in ways that raiders will find difficult to attack(this advice survives to the modern day in the form of Feng Shui, but originally it's immensely practical to have a wall just inside your main gate and avoid having roads leading directly to your door, not because it stops ghost intruders, but because it prevents raiders from just charging into your open courtyard before you can muster a defense) or treating illnesses...well that sort of thing makes for happy peasants believing in taoist sorcery/miracles.
Most of the common people simultanously believe in Confuscianism and Taoism. Buddhism hadn't arrived yet, or they'd believe in all three at once.
