This may be an odd time to quote Harrison Ford, but I once heard him lecture on the process of creativity (regarding acting) and he had an insight I never forgot. He said that basically if you want your acting (aka art) to be successful, you have to be true- your art must stem from something real and genuine. You can't 'fake' it or it will be fake.

I agree with that outlook, and for me, I can only sing a song I believe in and empathize with for it to work. If I am singing gospel that stems from a fundementalist viewpoint (which is far from my own) I may tweak a verse or word, but I truly believe in the uplifting and/or spiritual aspect of the song. It moves me. Or why else would I sing it?
And I have heard atheists who say they are moved by spiritual music, because there is something so fundamentally touching jmho in talking about the creative spirit of the universe, however you view it.

For me it comes down to - is music a true expression of the heart, or is it just decorative wallpaper. In truth, there's no right or wrong, no grade on it; but I prefer music from the heart.