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The way it was worded basically said that it had to be the national motto, thereby not making it a religious text to bypass the concerns you mentioned.
What I don’t understand is how the national motto can be a religious one without breaking the first amendment.
It hasn’t reached the Supreme Court for a decision, but lower courts have basically said that it’s not establing a religion because it’s used in a secular and patriotic fashion. (My interpretation of my understanding of the ruling).
https://en.m.wikipedia.org/wiki/Aronow_v._United_States
You can blame 1956 Cold War era Congress (red scare) and Eisenhower.