There’s another issue here: how old is the child? Can an elementary school child be presented with non-Jewish music? In this case, the parent has control about what the child hears. Obviously, you’re going to be careful not to expose the child to anything confusing.
For teenagers? That’s another story. Teenagers have their own preferences, usually strongly influenced by their peer group, and may not hold with their parents’ choices. In fact, for the sake of establishing their independence they may go directly against their parents’ wishes.
Two separate problems, actually.