When it comes to being sensitive to individuals of diverse backgrounds, the terminology that Percy learns to apply to the demigod world deals with similar issues to that of human discourse. He learns the proper way of addressing and referring to certain "demi-graphics," so to speak, with the help of his best friend and guide, Grover, a satyr. Apparently, "protector" duties include making sure your charge doesn't say anything that will get him into trouble, which makes sense when the wrath of mythical creatures is involved.
It's also just something that good friends do for each other — hold each other accountable for using oppressive or offensive language. One of the first suggestions that Grover offers relates to his own identity, when he informs Percy that the "politically correct" term for a half-man, half-goat is a satyr. (Percy has just insensitively, though not maliciously, called him a "weird hybrid man-goat thing," so the correction is warranted.)
Grover apprises his friend of the proper language in multiple scenarios. For example, the preferred way to refer to a cyclops, we learn, is "ocularly challenged." These comments might go right over a child's head, and when adults pick up on them, it's important to frame them as supportive toward groups of people pursuing their desired nomenclature.
