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Irish people were actually considered “non-white” throughout most of the history of race as a concept. They were only recently recategorized by racists when they felt their numbers dwindling and decided to expand the tent a little.
Irish people have suffered from a history of explicitly racist oppression; calling them “the oppressors” flies directly in the face of history. Their skin colour may be white, but the history of their relationship with race as a power structure is far more complex.
This does not mean that it’s impossible for Irish people to be racist themselves, or for Irish people to embrace “white” as an identity. Race is complicated; that’s exactly why trying to adopt simplistic attitudes to it never works.
But you do see how you’re very much engaging in stereotyping by saying that “They historically chose to address that by becoming cops” as if somehow a) all Irish people in America became cops, and b) the experiences of the Irish diaspora in America are somehow representative of all Irish people… Right?
Like, seriously, go ask some Irish people in Northern Ireland how they feel about cops some time. Depending on who you ask you’re guaranteed to get some wildly different answers.