Fuel Tank to counter you argument.  Yes, it is not wrong to  chose whatever song she wants to sing. But  it is wrong to say , I cannot sing this song because it is hindu. From what I have known from Christianity, it never bars you from singing a song or carrying out your job. A muslim doctor cannot say " My religion does not allow me to carry out my work on christian patient" and vice versa. 

May be this video will open and explains what is wrong when  you bring religion to your duty.