Did Americans not see Italians as the inheritors, or at least analogues, of Roman identity?
This also applies to a lesser extent to anti-Greek sentiment.
title edit: *has there
The early 20th century and late 19th century attitude towards the collapse of Rome often included the theory that racial mixing (from Africans, Arabs, and Berbers, etc.) in Italy was what weakened Rome. Now this is blatantly ridiculous to suggest, but this was the time of racial science, so it was a widespread theory. Many saw the Italians, especially those from the South who were more genetically diverse (and were over 3/4 of immigrants to America from Italy), as not the Romans of the past.
It also doesn’t help that, due to statues and the like, most Romans were perceived as white and pale, contrary to the fact that Rome was very diverse. This perception didn’t match the appearance of the swarthy Italian immigrants and their features.