As a general rule, my suggestion would be not to put them on secular music restriction, but rather to teach them discernment, both of lyrical content and musical quality. Start a conversation about what artists/songs are good and bad and why. Help them start thinking for themselves what music reflects beauty, creativity, artistry, truth, righteousness, etc. The reality is that there is some great “secular” music out there worth repeated listens and some poorly written and performed “Christian” music out there not worth the airplay they receive on Christian radio; and vice versa.
Secular music restriction may be a necessary beginning just to get them to stop filling (and shaping, and marring) their souls with unbecoming lyrics. But, depending on the kid, strict restriction could lead to rebellion. She may not listen to secular music at home, but she will when you’re not around, and later when she grows up and she’s on her own.
Teaching discernment is a lesson they can carry over into all areas of life. It’s not a tug of war. Since the goal is teaching them to make good media choices, they are involved in the process of choosing which music should be allowed on their iPod and will be able to explain to you why or why not. Whether you’re persuaded on any given song or artist is your parental judgement call.
Also, it helps to remember that beauty is not just in the eye of the beholder. Good music is good music and should be appreciated. Nevertheless, we all have handicapped musical taste buds (teenagers especially, but parents too) which keep us from enjoying some kinds of good music. On the other hand, some of the best music being made today is being ruined not by our lack of ability to appreciate it, but by the artists’ lack of sense and spiritual depravity when out of the abundance of their hearts their mouths sing lyrical crap. (I’m thinking of the pie in The Help). Too many people are ignorant of or ignoring that key ingredient.