You are not required to attend that school, therefore they can pretty much require any conditions short of illegal activity as a condition of attendance.
As a kid, while I understand your being upset with the rule, that carries much less weight than that your mother is unhappy with it. Obviously, you have talked about the issue, and are considering changing. Look at your options together, and weigh the good and bad points of each choice. The quality of education is very important, but the social aspects of school are also very important. The lack of adequate proofing for the rulebook is not necessarily indicative of the quality of the education. However, it does raise a red flag that you should address.
I personally would not be happy with any school that tried to usurp my role as parent, and my child's behavior off school grounds, and off school time is none of their business. If and when it has direct impact on school (such as homework), then it has some bearing.
I think the idea of teaching about cyber space and appropriate and inappropriate use is a fantastic idea.