In the real world employers don't and or legally can't force you to censor your personal PC's at home, where they are not paying for the Internet Service.
Too bad you posted AC, that's worth some mod points.
Reality is, the school has no jurisdiction over what the student does off school grounds. Including what they do on their computer.
IANAL, but if you want to control what they can and can't do with the computers, you have to keep the computers on school property. Otherwise, I suspect you would be running into legal issues.
The above post is also right in recognizing that no matter what you do to try to prevent the students from doing certain things on the computer
Anyone can make an omelet with eggs. The trick is to make one with none.