I should have read this first, as you pointed out  I use 1956, a time of the great communist paranioa, the rhetoric of the disgraced liar McCarthy.  This knee jerk populism probably fed this 'In God we Trust' as a way to identify the nation as morally different from the Godless communist nation.  If this phrase is taken as a Christian God, it expresses the same intolerance that you recognize in t Muslim nations that integrate religious dogma with political control.

I'm not sure where you stand on populism, but I suspect you feel as I do, that current political, or social, trends shouldn't be enshrined over the judgement of the founders who were on the cusp of the Age in enlightenment, Age of reason.

https://en.wikipedia.org/wiki/Age_of_Enlightenment