How come the sentence 白いのは、高い is ok, but the sentence 学生じゃないのは、学校に行かない is not? Wouldn't the second sentence just mean "the one who isn't a student does not go to school"? On Tae Kim's grammar guide, he says that to replace a noun with の, the sentence needs to be "about the clause and not about the noun that was replaced." I'm not really sure what that means, so can someone please explain it?
Statistically speaking, I think it's true that 学生じゃないの usually refers to a state ("not being a student"), whereas 白いの usually refers to an object ("white thing"). However, the correct meaning largely depends on the context.
Please remember that の meaning one usually replaces a noun representing an inanimate object (i.e., 物). Sometimes の can also represent a human being, but it's not very common, and it sounds rough and/or condescending (similarly to 奴). For example, it's possible to say "学生じゃないのが学校に来るな!" or "もっと強いのを呼べ!". But it's safe to avoid this usage if you are a beginner.
の also works as a nominalizer. Both 学生じゃないの and 白いの can represent a state. For example, you can say 学生じゃないのを悔やむ ("to regret not being a student") and 髪が白いのを心配する ("to worry about someone's hair being white").