I think there are a few red herrings here. Ignore all the stuff about modes, it's to do with the range. The fact is simply that the range of many tunes makes it difficult or impossible to play them on a whistle that is in the key of the tune. Drunken sailor is one such tune: you can't play it in Bm on a D whistle because the whistle's lowest note is D and the tune goes down to B. You can't put it all up an octave or you'd run out of notes at the top.

The whistle player would play many ordinary major tunes in G on a D whistle for the same reasons. Any tune that goes below the tonic note(do) won't be playable in D on a D whistle.

You will find that some whistle players can't explain this to you, as they just play instinctively and have never really thought about it, so don't be surprised if you get puzzled looks when you ask them.