If you want to show off that your children are Frum, you should announce that they don’t have library cards, and that you won’t do a shidduch with someone who does.
Hat Tip: Daas Yochid 🙂
Seriously, I wouldn’t let my (smaller) child take books out without supervision of some kind. Luckily, our local library has an option where a child can only take out children’s books or DVDs, so I’m less concerned.
A teen is his/her own subject, and each one needs to be decided on his/her own merits.