Huh? Having fins isn’t a nationality? Irish was just an example of an adjective. Not sure why you are bringing it up?
trans people are self-defined so it’s not something outside their control.
Sorta, but the statement seems to show a pretty relevant and significant misunderstanding. Trans isn’t like an easily externally identifiable trait like skin color (technically an autopsy could potentially provide evidence for being trans even in those who’ve never taken hormones or done any gender-affirming surgeries, but like we are talking about correlates, not defining features). But like neither is autism. You find out basically by asking.
For sports, some leagues have started dealing with the existence of trans people and hormone-doping cis women by simply making sports divisions include hormone requirements. Its not really about whether the person is trans or cis though, so it means some cis women who aren’t doping get excluded from cis women sports with such rules.