I also disagree with the idea that it was added for religious grounds. More accurately, it was added on ideological grounds in an "Us" vs "Them" distinction during the Cold War. We were trying to show how non-Communist we were, not spread the Gospel of Christ or something. Had they said they all loved Coke, we'd have slapped a Pepsi can on the dollar. If they put Transformers on their coins, we'd have added Go-Bots. And been that much the poorer for it. Since the Soviets were seen as "godless", we had to play up the God card.
So we should modify it, adding a footnote?
In God We Trust*
*Not intended to be a factual statement