That's why it's important to know what information is available about you. Not necessarily, but you should be as careful as you would be when visiting a strange city. Your best defense is learning what can be done to you, and what you can do to prevent it. Some filters are rather clumsy in blocking sites. Some parents prefer to use tracking software that keeps a record of every site the child visits.
Some parents forbid their children to use the Internet without direct parental supervision.
Take into account your child's age, character, and your own family's standards of acceptable behavior when planning your defence.