A quick question: Does a just-intoned whistle sound way off when playing with an equal temperament instrument (such as guitar), or do the two sound OK together?
They sound OK. The guitar is a few octaves lower than the whistle, and it doesn’t produce continuous sound, so you shouldn’t have any nasty beats.
Where you might get in trouble is playing with another whistle that’s not just-intoned, because then you have 2 instruments that produce continuous sound, and they’re playing on the same register. In practice, you would automatically use variations in the air pressure and the air stream to bring your instrument closer to the other one, and you might not hear anything too bad either.
Where you really get in trouble is with pipe organs, because then the player has no control over the intonation. That’s why tempered tuninigs survived a lot longer on organ than other instruments.