I think the only real limitations concern range, damn those fiddlers and box players.
Is a tune composed on the pipes a pipe tune? Sure. Flute for flute? Of course. Should a whistler avoid playing a fiddle tune? Not for that reason. The main question for me was always, does it sound good? There are fiddle tunes I wouldn't play outside of sessions because I just didn't like how they sounded on flute, but folding out of necessity wasn't always the reason. And to be fair, sometimes it was. Odds are that a tune composed on your instrument will be relatively easier to play than on any other instrument, but in the end it's not axiomatic.
Are there tunes specifically composed for certain instruments? Yes. The late great box player, Paddy O'Brien of Nenagh, composed some of his tunes specifically with the uilleann pipes in mind. I would say that's ample reason not to worry whether you'd be overstepping bounds in playing them, if the question occurs.