I don't think it's about believing, but connecting. If a song means something to you, even if it's not what you may think it originally was intended to mean, why shouldn't you sing it? If it means nothing to you at all, you have no business singing it.

I remember reading once that when you are listening to music you should be a Mason when you listen to Mozart, a Pagan when you listen to Wagner, a Communist when you listen to Shostakovich etc.(I paraphrase but you get the point I hope)