Yeah, it depends on the whistle. BUT, and this is a big one, C natural in Irish music does not necessarily have to be the perfectly tempered C nat you may used to if you are coming in from the assumption that all instruments and music are using equal temperament.
In Folk Music and Dances of Ireland, Brendan Breathnach, a very respected historian, UP player and collector of Irish trad, defines a C natural as falling “halfway between B and D.”
You have to ponder that one for a while for it to sink in when you read it. In that one statement, he is revealing that you aren’t in London or Paris anymore regarding scale tones. He also talks about F natural being a special note as I recall (don’t have the book here).
Others here are much more expert about tunings within the scale and there are threads about it. But my practical solution is this:
I understand and accept that I am not confined to just one C natural when playing this kind of music. I have choices. In general, if I am playing a tune that is in Aminor, I definitely want that half-holed version, especially in airs. In other cases, like D Mixo tunes, like Banish Misfortune, I rather like the sound of the sharper Cnat of the oxxoooo variety. The Old Bush is another tune that, to my ears, the sharper Cnat sounds better. I have heard pipers use a C sharp for it in fact.
And practically speaking, if you are playing fast music, and the oxxooo works better in the passage, go for it. Some would even just use the C sharp. Joanie Madden mentioned that one evening in chat because I was asking her about halfholing versus oxxooo.
The whistles I play (Burkes and cheapos) do not have a real C nat at oxxooo so this is where I am coming from. I understand from reading that other makers do have a more “in-tune” Cnat with that fingering. I am satisfied with my approach with what I have and what sounds good to me. I will have to adjust this thinking if I purchase a whistle that has a different option.
My two “cents.” Hope it helps.