One thing you can never depend on racists for is consistency.

There are political cartoons drawn by fascists from the 1920s that attempt to stave off accusations of racism by pointing out that they include Italians (then show Mussolini as a racist caricature of a black man), as if Italians aren't widely considered white.

If you look at how the British and later Americans talked about the Irish "people" or "race", you'll note shocking similarities to how they talked about Africans, Native Americans, Asians of all stripes, etc etc. Explicit skin color rarely came up.

Racism, especially old timey racism, is all about "how do I define my group as 'good' and everybody else as so bad that I can treat them worse?"

Just for curiosity's sake, when you talk about Italians being widely considered white what context is that in? Because you later talk about anti-Irish racism in the US in the 20s and 30s and the experience was pretty similar for Italians in the US in that time period as well. I have living relatives that can give you firsthand accounts of open, organized, violent anti-Italian racism in Pittsburgh pre-mid WWII.