Whiteness is a social construct, not an inherent genetic trait.
One of the problems with the polarized way we talk about the history of racism is that it swallows subtleties. The reality is that no one is white. We're all human beings, and we all come in varying shades and hues of brown; from pale and pink-ish to a deep brown that looks navy blue in the shadows, and many olive and peachy and cinnamon tints in between.
"White" is an invented concept, and it the definition has varied to includes different groups over the few hundred years it's been in use. The Irish used to be very much on the outside of "white". As were Italians and Spaniards, and Poles, and others we easily assume are "white" today, when we have a broad skin-shade based understanding of the (fake) divisions between "races".
In fact, the English used many of the same tactics of colonization against the Irish and the Scots as they later did against Indigenous peoples on this land. Including pushing them off their lands and away from their traditional food sources; starving them by withholding other foods, while also extracting foods and profits from their lands; forcibly 'schooling' their children, and beating their languages and cultures out of them. Oh, and the English were aided and abetted in these efforts by a church that purported to care while sharing in the exploitation...
...does that sound familiar?
It's true that the Irish and Scots in many ways were co-opted into colonization, having moved to this land by the hundreds of thousands, fleeing English occupation, and it's true that they sort of gained 'whiteness' when they arrived on these shores.