In my own experience it has been this way for at least fifty years.
Until the USA becomes a theocracy (exclusive) instead of a democracy (inclusive) it is the way it should be in
public institutions.
Private institutions, as always, can be as exclusive as they want.
It would probably have been so much simpler if the founders of the US had declared an official state religion... but they didn't. Aside from the First Amendment to the Constitution of the United States there is also Article IV, paragraph 3 which says:
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious test shall ever be required as a qualification to any office or public trust under the United States.
(emphasis added)
Do you also think that this was not the way it was or should be?