The relevant scholarly literature seems to have started with Noel Ignatiev’s book “
How the Irish Became White,” and taken off from there. But what the relevant authors mean by white is ahistorical. They are referring to a stylized, sociological or anthropological understanding of “whiteness,” which means either “fully socially accepted as the equals of Americans of Anglo-Saxon and Germanic stock,” or, in the more politicized version, “an accepted part of the dominant ruling class in the United States.”
Those may be interesting sociological and anthropological angles to pursue, but it has nothing to do with whether the relevant groups were considered to be white.
Here are some objective tests as to whether a group was historically considered “white” in the United States: Were members of the group allowed to go to “whites-only” schools in the South, or otherwise partake of the advantages that accrued to whites under Jim Crow? Were they ever segregated in schools by law, anywhere in the United States, such that “whites” went to one school, and the group in question was relegated to another? When laws banned interracial marriage in many states (not just in the South), if a white Anglo-Saxon wanted to marry a member of the group, would that have been against the law? Some labor unions restricted their membership to whites. Did such unions exclude members of the group in question? Were members of the group ever entirely excluded from being able to immigrate to the United States, or face special bans or restrictions in becoming citizens?