Why has the far-right not called out the myth that Irish, Italians, Slavs, etc. were not considered "White" in America and the Anglosphere at large?

When people make this claim, they never cite any actual evidence for it. The closest I've seen for evidence of this is a private diary entry from Charles Dawrin's brother who said the Irish looked like "White chimpanzees" after a visit to Ireland. I shouldn't have to point out that even if this piece of evidence, the Irish are called "White".

Another piece of evidence often cited is the book "The Passing of the Great Race". It is claimed that this book described non-Protestant immigrant groups as "non-White". But I read this book, and not only does the book list the Irish as "White", it places them in the highest caste (Nordic). It also claims all Europeans are "White", including Italians, just in different categories.

The discrimination Irish Catholics faced in America was entirely limited to the North of the country where divisions were by religion (Protestant WASPS vs. White Catholic immigrant groups). In the South, it's well known by historians that the Irish Catholics integrated well into the White vs Black society of the Antebellum South and became reliable Democrat voting slave owners. Irish, even in the North, were known for their sympathies for the Confederacy for this very reason because they knew they would be better off in an America that was divided by race rather than religion.

Italians and other non-Protestant immigrant groups faced similar issues. It was never about race, but about religion. In fact, it's forgotten that German Catholics were also not welcome in America. The Know Nothing Party didn't just target Irish and Italian Catholics, German and French Catholics were also attacked in their literature. Of course, no one tries to make the claim that they did not consider the Germans or French "White".