How did events during the period 1880 to 1920, reinforce or contradict the image of the United States as a "melting pot" for races and ethnic groups?
The events of this time do more to contradict the image of the melting pot than to reinforce it. The reason for this is that this was the time when the immigrants were coming to America in large numbers. The immigrants had, in general, not had enough time to "melt."
Because of this, there were not yet many Jews or Italians who had assimilated into mainstream America. Instead, they settled in areas that were dominated by people from their own country and even from the same villages they had come from. They formed self-help organizations among people of their own ethnicity.
This was a time when the melting pot had not had enough time to do its work, which is a major reason why the 1920s would see immigration restriction laws passed.
By looking at the numbers of immigrants from Europe and Asia one might wonder if the ethinic groups homogenized into Americans, but cities have ethic neighborhoods. My great grandmother grew up in Missouri. She says that parts of Saint Louis had people who spoke Italian or German and little English. My grandmother says the same about New York City. Today, here in California, some neighborhoods speak Mandarin or Spanish, but little English.
However, my great great grandparents came from a dozen different countries. On Saint Patrick's day we're Irish. On Columbus Day we are Italian. During Tet we are Chinese.