Aries has a fine take on it. Judging by the words in the original post by Ofcourse, it seems that the parent currently does not have a great bond with the child. That being the case, doing anything to strengthen that bond would be beneficial. Once a bond a forged, then the parent can decide where to make boundaries and where not.
Also, it depends on what type of secular music the child is listening to. If it contains lyrics that promotes immorality, drugs, or anything potentially harmful, having a parent listen to it with the child may not be the best way to create a bond. There can, and will, be other ways to create it. But if the lyrics are fine, or any sort of instrumental music, a parent can do well to join the child by listening and having an interest in it, even temporarily, to create that bond.