I should have said "genetically or biologically" -<quoted text>
Yes - but culture is a part of ethnicity. And as long as you consider yourself Irish (even if you dont look/act Irish (whatever that means) AND you have the famly history, you ARE Irish. But if you forget you are Irish, and noone "reminds" you, you are no longer Irish, ethnically/culturally or otherwise.
These things dont always fall into perfect boxes. But they are not that complicated either.
When I was young I remember going to Jewish youthgroup conferences where they sat around at a table trying to decide whether we were Jewish Americans or American Jews. People get PhDs on these types of topics, but are they really usefull at that level of detail? I never thought so.
I think they've checked people's DNA and were able to tell from where and who they descended.
Like, even if someone was raised by wolves, you could look at them and tell who "their people" were. Not all the time, but sometimes.
Sometimes I might think someone looks Greek or something, and they turn out be Italian or Jewish - not an exact science.
My pastey Irish skin could also look British or whatever.