The “immigrants from a wide variety of backgrounds” in the 1920’s and 30’s were from western cultures, namely Europe. So the variety wasn’t as large as what we’re experiencing today.
Think though how horribly the Irish were treated.
If one chooses to look at the segregation of the black population prior to 1964, it could be argued that the civil rights laws of the 60s allowed the blacks to be Americans. And that no matter how many generations of blacks had lived in America prior to 1964, that with the equal rights laws of the 60’ the blacks were 1st generation American immigrants. New to the States...as equal citizens.
And they all had there kids assimilate.