However, the statement “some white people aren’t white to racists” implies that skin color IS the defining concern. And the direct comparison of white-on-white mistreatment to white-on-nonwhite racist mistreatment is a grasp for moral equivalence.
If Irish immigrants were truly considered nonwhite, maybe they would have been hunted down and slaughtered like indigenous peoples, or separated from their children like African slaves. But these things did NOT happen, and I hold that it is inappropriate to describe the Irish as “not considered white”. Of course they were white. Nobody, not now and not in US history, would describe them as nonwhite. Sure, some people didn’t like the Irish, but that’s a far cry from considering them to be a different race or color.
Irish and Irish-descended could vote, they could go to court to seek redress of grievances, they could marry who they wished, they were not confined to reservations, they could have children without fearing that they would be taken away. Indigenous, African, and sometimes Latino and Asian peoples in the US did not always enjoy such rights, but white people almost always did.
I brought up chattel slavery because the commenter said, “in the US”, and the exemplar for white-on-nonwhite racism in the US is chattel slavery of black Africans. But if one prefers to consider the mistreatment of other nonwhite racial groups, you could certainly hold any of them up to the way Irish were treated, and I daresay that you would have a hard time finding any dimension of mistreatment in which Irish or other white minorities were treated worse than nonwhite peoples.