Yes in the key of D the note F# is the Major 3rd and thus should be 14 cents flat according to Just Intonation.
Now let’s switch to the key of G: the note F# is now the Major 7th and should be 12 cents flat.
How about the key of A? F# is the Major 6th and should be 16 cents flat.
Everything is great so far, isn’t it?
But wait!
In the key of E minor the note F# is the Major 2nd and needs to be four cents SHARP!
And in the key of B minor the note F# is the Perfect 5th and needs to be two cents sharp.
The point is, it’s false to take the Just Intonation of one key and apply it to a different key. That’s misunderstanding the entire point of what Just Intonation is. It’s precisely these conundrums that eventually led to the adoption of Equal Temperament, as lousy as ET sounds to somebody who is used to JI.
Now, I freely admit that bagpipes are a special case, due to the drones.
Thus the uilleann pipes, because they have drones all playing the note D, to have each note of the chanter precisely blend with the drones needs to have the chanter tuned to Just Intonation in the key of D, regardless of what key the particular melody is in. So it doesn’t matter that the piper is playing a tune that happens to be in the key of E minor; that F# still needs to be 14 cents flat in order to be an in-tune Major 3rd with the D of the drones.
Fiddles are a different case, because they in effect have four different potential drones, each of the open strings. Happily one of the four is the same D that the uilleann pipes have, and the other three are going to be at most a couple cents off.
Anyhow let’s not forget that tuning is situational: no note is “in tune” in a vacuum, and any note not in a vacuum is “in tune” if it agrees with the surrounding sound.
So an Irish flute with the F# 14 cents flat will be “in tune” when playing along with an uilleann chanter which has its F# tuned 14 cents flat (to match the D drones), but that same flute will be “out of tune” when playing along with a banjo, guitar, mandolin, piano, ET tuned box or accordion, etc.
I think the whole “ET v JI” controversy is overdone. I use my uilleann chanter in non-trad situations far more than I use it in trad situations and I’ve always had to keep in “in tune” to a strict ET scale. Even in trad situations I’m usually playing with a guitarist so the ET sounds better.