Some will, even if they don't believe it all.
yup I will be singing carols until the cows come home between now and the week before Christmas, including at a concert and several charity fundraising events.
Why? Because I love singing and it is completely irrelevant whether I believe the words or not (I don't by the way), it doesn't affect my enjoyment of singing.
And earlier this month I sang at a concert with a piece with words by Blake, and guess what, I'm not a Blake-ist. Also there was a piece about the First World War, but I am broadly a pacifist. Another written to celebrate a military victory by the British over the French, yet I am certainly not a Francophobe who wants to see them soundly beaten - again, far from it.
So I really don't understand your point BA.