Basic terminology
Before we go deeper into patterns of behavior, let's first have a look at the linguistic part, at the basic terminology in Mandarin related to politeness: If someone is polite, Taiwanese will say 有禮貌 (yǒu lǐ mào), which literally means "to have a polite/ceremonial appearance." Another word for politeness or courtesy is 客氣 (kè qi) and literally means "guest-like atmosphere." It's used in the standard reply you're welcome as 不客氣! (bù kè qi) after someone says thank you, or in situations where the host wants you to be less formal. They would say 不用客氣! (bù yòng kè qi), which means something like "don't behave as formally as a guest." My mother-in-law will say that to me when she cooked a lot of food hoping that I eat as much as possible, and not care about appearing impolite. An alternative way to say the same would be 不用多禮! (bù yòng duō lǐ), literally meaning "don't need to be so polite/ceremonial." When someone is rude or impolite people will say 沒有禮貌 (méi yǒu lǐ mào), literally "to not have a polite/ceremonial appearance." A more direct way to say the same would be 很粗魯 (hěn cūlǔ), literally "being very rude.