We already have Unitarians.
Hymns I actually heard at a brief stint at North Texas Church of Freethought (atheist):
“Imagine” by the former Beattle
“All We Need Is Love”
“Building a mystery” by Sara McLaughlin
Jimmy Buffet My head hurts, my feet stink and I don’t love Jesus
That’s EXACTLY what I thought. (it’s nicer than mentioning the Episcopalians, but there are many atheist bishops out there.)