I think the perfect case in point is the Pledge of Allegiance.
It was instituted in 1892 as a way to 'normalize' the immigrants coming from Europe.
But since the original version referred only to 'the flag' without further description, it occurred to people that the words 'of the United States' needed to be added to make sure people weren't saluting some foreign version.
Also, originally 'pledgers' were required when saying 'the flag' to raise their arms in salute, with palms upturned.
But with the asscendency of Hitler in Europe, this started to look problematic, so it was decreed that hands should remain over hearts.
Then when Communism became the great threat, Congress inserted the words 'under God' in 1954.
And of course, there have been court battles to remove this ever since.
So my conclusion is that it's hard to determine 'normalizing' in any consistent fashion when the definition of 'normal' continues to change.
And the thing that separates us from China most of all is that we, as a country, can continue to argue about all this.