From my email:
Does the school have the right to make you take out or cover up piercing?
If it’s a public school, then the First Amendment prevents them from not allowing you to express yourself in a way that’s silent and non-disruptive (see the Supreme Court case Tinker v. Des Moines School Dist. where the school could not keep the students from wearing armbands). However, regulations on things like clothing and dress code are permitted.
Piercings seem more like armbands than like clothing, so a public school probably can’t tell you to take them out or cover them up. However, I don’t think there have been any court cases specifically about piercings, so it would be hard to say for sure.
(Answering questions like this is a lot of fun and sort of makes me want to study law. Knowing the geeky details of something like programming or cryptography doesn’t have the same impact.)