No, children should not be allowed to take balaclavas into school. Balaclavas are used in such things as armed robberies and other criminal activities. Do you really want your child to be wearing something that criminals wear, i certainly wouldn't! It could encourage people into crime. It also hides peoples identities, easy to pretend hey are someone else. This could result in a massive problem for teachers and other staff trying to teach.
The problem is, very few people in the United States have the ability to avoid feeling threatened by a balaclava. Due to its extensive use in robberies and murders, it has an unerasable stigma in the urban environment. Simply, no one will think you're a good guy if you wear a balaclava to school.