Puritan Board Junior
As to exposing ourselves to secular music, we Christians are privileged to use biblical discernment - our sanctified common sense. If the lyrics appear to be offensive - turn it off, or put on something else.
As with anything pertaining to Christian liberty I agree that this is the key. Although I do think that the OP is a question worth thinking about. I say this as one that has a few Aerosmith (not Walk this Way), Def Lepard, and Bon Jovi songs on my iPod. What few songs like that I listen to I usually find have sentimental ties to my college days or something like that. But I often find myself wondering if a guy like Jonathan Edwards or Thomas Watson or John Flavel would listen to some of the stuff we listen to. For that matter I wonder if the Puritans would have excused some of the other secular things we tend to excuse in the 21st century.
I still say it's a matter of Christian liberty and Richard's response above hits the nail on the head. But this has been an interesting thread nonetheless.