This "Irish/Italians weren't White" propaganda is used to try and normalize non White immigration. These people were always legally considered "Free White Persons" and, like you said, it was mainly the amount of people coming in that was an issue. Furthermore, people didn't trust Catholics. But no one ever considered them non White.
Also why would the US name 1 million things after an Italian named Columbus?
If this is what is considered "Absolutely HORRIFYING" to some, they've got a big shock coming
They need a real taste of Diversity
Under Natural Law
Stupid can be a Capital Offense