My mom doesn't like secular music, but country is ok. I've tried to get her to realize, or more like admit, that it's no different .. except the tunes and tone of voice .. all talk about sex, drinking, and cheating .. seems the "beats" on the secular music are what offend people or something. Hasn't (and prolyl won't ) happen yet.
I have a hard time dealing with people telling my kid what to do .. but the fact is, when they are at other people's houses you can't tell them what they will or won't do in their own home. If she doens't want secular music being played in her home .. you can't very well make her allow it .. would work the same if she tried to tell you not to do something in your house.
I don't agree with it, really (to a point .. some music is not kid worthy .. with all the sex talk and cursing and shit .. they don't need to be singing along with that, yanno) but I don't see how you can't stop her from exercising a rule in her own house.
Having kids is a difficult battle, epsecially when you have the "extra" parent to deal with.