I think we kid ourselves when we suggest that a secular government is non-religious.  Indeed, the impetus for, e.g., forcing prayer out of schools was anti-religion.  

Prohibiting prayer in schools is a government violation of the right of People to practice their religion.  Allowing prayer, but not requiring it, is not forcing anyone to do anything.  But the anti-religion folks have twisted the Constitution successfully to convince the Court that the government cannot allow religion in public or publicly-funded places.  Nonsense. 

If the People want religion in the government, then openly religious folks will start winning elections.  And if a swath of people with the intention of taking over the government should start immigrating to the US, the government should be allowed to stop them from coming using its power over immigration (the 1st Amendment does not apply to those who are not here)