There are so many cases of promoting Christianity by the US government, a few cherrypicked cases of “trouble” doesn’t disprove any of this.

• “As a matter of historical tradition, the words ‘under God’ can no more be expunged from the national consciousness than the words ‘In God We Trust’ from every coin in the land, than the words ‘so help me God’ from every presidential oath since 1789, or than the prayer that has opened every congressional session of legislative business since 1787.” https://en.wikipedia.org/wiki/Pledge_of_Allegiance#Legal_challenges

Also, the US print religious indoctrination on their currency: https://en.wikipedia.org/wiki/In_God_We_Trust