Does your existing ILS allow for family accounts or linked accounts (parents can see what is on their children's accounts because they are financially responsible for those accounts)?
The libraries where I have worked have always made it a policy of not acting in loco parentis - it is the parents' job to know what their kids are reading and watching - not ours. If you take responsibility for keeping children from watching videos intended for a more mature audience, then parents may expect you to also take responsibility for keeping their children from reading materials intended for a more mature audience - and how would you do that?
To have an effective age comparison system, as you suggest, you would find yourself in a position of needing to collect birthdates for members in order for the comparison to be up-to-date (generally not advisable for privacy reasons), and you would probably also have to limit members' ability to update their own accounts (teens could go in and change their birthdates or the permission setting).