At the risk of confusing a subject that is already pretty much unintelligible, I’d say that whether an instrument is transposing or not really just depends on how you perceive it.
For example, we might say that in orchestral terms an Irish flute (D in our terms) is not a transposing instrument because when we play the all holes closed note, which we think of as D, it actually comes out as D. In orchestral terms they say that this instrument is in C, or concert pitch, because the notes that are produced when you use the correct fingering for a written notes are at the pitch you expect.
So, in this sense, if you get a Bb whistle, and think of it as a Bb whistle that plays Bb when you cover all the tone holes and blow, then it too is a concert pitch instrument, and hence is also in C.
However, if you think of your Bb whistle in the same way as you think of your D whistle or flute, then when you play the all holes closed note, rather than getting a D you will get a Bb. So in this case, the instrument will appear to have transposed the note up 8 semi tones. So rather than being in C, as the D flute was, it will be in C plus 8 semi tones, which is Ab. Somehow, I never personally find this way of thinking about it very helpful. Just sayin.
It really just comes down to how you perceive the instrument and how you interpret sheet music. Do you do the transposing yourself, or do let the instrument do the transposing.
You could equally well view your range of trad whistles/flutes as being transposing instruments in a key one tone lower than the key we usually use to describe them. Or you could think of them as all being non-transposing instruments and recognize the actual scale each plays.
Where is gets completely mind boggling is when you get stuck in the middle between these two mindsets and try to use them both at the same time. 
Learning and playing by ear avoids all of this entirely, because its really just a symptom of using written representations of music and then not rigorously sticking to it, i.e., tying the written representation to the note actually sounded.