Yes, it is possible. In order to do it, each person using the computer needs to have their own user account.
A user account is like a separate space within the computer just for that person. They have their own username and password to access it, and can install whatever software and set whatever preferences they'd like, without affecting anyone else on the computer. Because the computer treats each user account as its own independent space, the parental controls settings for that account don't impact other accounts.
This is particularly useful because it lets parents set different restrictions for different children. For instance, a 17-year-old can probably download and view different kinds of content than a 10-year-old. And parents will probably want no restrictions on their options. (Though it's worth remembering the parental controls only restrict what can be accessed at iTunes, not on the rest of the Internet.)
Instructions for creating user accounts on some popular operating systems:
With the accounts created, tell everyone in the family their username and password and make sure they understand that they must log out of their account when they're done using the computer. Parents should make sure they know all of their kids' usernames and passwords.
To apply content restrictions to kids' iTunes, log into each user account and configure iTunes parental controls. Make sure to protect these settings with use a password other than the one used to log into the user account.