The TL;DR on that is that whiteness is a social category, not an objective observation of human beings and their differences. For most of American history, as an example, Anglo-Saxons, Dutch/Low Germans and Scandinavians were considered a superior race to the 'alpine' and 'mediterranean' races of High Germans, Spaniards, and Italians. Irish weren't Anglo-Saxon, they were Celtic and were thus considered inferior. The racism people observe when they see 'Irish need not apply' signs or slurs directed at Italians in the 1800s were because those people were not considered 'white' at the time. It's an over-simplification, but these groups needed to be incorporated into the dominant group before they would be given the treatment we generally think is normal for white people.

Which is very jarring to us, since obviously Irish and Italians and Bavarian Germans are 'white'. But it literally does vary, and the entire purpose of the category is to render people inside of it superior by virtue of belonging to it, it's a category that exists to express supremacy.