There is a fine disctinction between religion in general (and its role in America’s history) and the state favoring a particular religion or church. I have no great problem with “One Nation Under God” or even “In God We Trust”.

The Supreme Court ruled as such over a deptiction of the Ten Commandments at the US Capitaol, which showed them in the context of their role in developing the law in history.
And we cannot ignore or deny the role that Christianity played in our nation’s development, but at the saem time, we must continue to stress that freedom of religion and separation of church and state are among the cornerstones of our democracy

The bit with the Muslim woman’s picture ID is, in my assessment an example of where the law trumps religious convictions: if she has trouble with it then she has the option of just staying at home.