Down the hill at GW, former professor Jessica Krug--a white person from Kansas City--spent her career posing as a person of"Afro-Caribbean Identity" with a New York accent. After being exposed, she resigned; her department said they would pursue her termination otherwise.
I have not myself posed as belonging to a different race, but I have at times not spoken up and instead allowed myself to pass as a member of difference race. (You can read a paper about the ethics of doing so here, by former philosopher Dan Silvermint.) In particular, I have allowed people to think of me as white. However, starting now, I will no longer do so, and indeed, will actively file bias reports against anyone who refers to me as such.
Originally, the Irish were seen by whites, especially British/Anglo-Saxon, Germanic, and Nordic whites, as an inferior "other". The British in particular eyed Irish lands with greed and envy. Much as they conquered and enslaved so much of the world, they conquered, displaced, and dispossessed the Irish in their own lands.
Irish culture was squashed. Clan identities were purged. The Irish language (often incorrectly called "Gaelic") all but vanished as English was forced upon the Irish. Catholicism was suppressed, though England's brutal methods in the attempt to pacify the people met with such resistance that they failed to transform the country into a Protestant stronghold. England exploited its people and its resources. It installed colonies under the Plantation system and ensured that the ruling and propertied classes were white Protestants. Natives were turned into poor peasants and their poverty was taken as proof of their otherness and inferiority. Not surprisingly, many Irish turned to servant roles as a means to escape poverty. There was no doubt in the English mind that the Irish were a separate, inferior race.
Many of these conquered, colonized peoples fled to the Americas in hopes of a better future. This was especially true during the Great Hunger--a famine caused and sustained far more by bad British policies than by mere crop failure. In the Americas, of course, the Irish faced discrimination, rejection, and persecution, as the English and German whites continued to see them as "other", as unclean, unfit, and criminogenic. Karl Marx famously disparaged the Irish as drunken criminals who couldn't even benefit from higher wages. Even in the 20th century, early progressive economists defended policies such as minimum wage laws with the expressed goal of disemploying, starving, and eliminating undesirable races such as the Irish. (This is perhaps why I am less impressed with people advocating such laws today, when I know these principles were intentionally devised as a means of starving my grandparents to prevent me from coming into existence.)
After long struggles, and despite the rampant mistreatment, the Irish diaspora in Canada and the US emerged as successful. Today, Irish-descent households in the US are significantly richer the US average and than English-descent households. I'm not sure why. Perhaps in the face of oppression, Irish immigrants developed better norms which enabled success. Perhaps the progressive's eugenicist policies worked, and the more functional Irish immigrants were disproportionately likely to have kids who survived to have kids of their own.
By the way, for people living in Ireland who say Irish-Americans aren't really Irish, please keep in mind the distinction between Irish citizenship (of which many of Irish-Americans are technical eligible) and nationality vs culture vs ethnicity. This is a discussion of ethnicity. It's true that colonialism and famine led to a large number of Irish ethnic individuals being born and raised without Irish nationality or culture. Further, while many Irish Americans are only partly Irish, keep in mind that we don't say that African Americans are not really black because they have other other non-black ancestors. Barack Obama is 50% white by ethnicity but we still say he was the first black president. He is thus whiter than I am if we're using genetics as a means of determining race.)
Irish people in the US and elsewhere now pass as white, and indeed, most are now inclined to call them white. This is unacceptable practice. The English had long sought to erase, eradicate, and replace Irish identity by making the Irish--at least the ones they deemed fit to survive--British and English.
To call an Irish person white is thus to participate in British colonialism and to work to erase Irish identity. It is unacceptable, shameful, racist, colonialist, and imperialist,
Note that non-Irish people do not get a say in this matter. You do not get to police the boundaries of Irish racial or ethnic identity. Your job, especially if you are of English ethnicity, is to be an ally and to listen, nothing less.