I also find out of tune music extremely distressing, and can't stand it. My ears actually have this weird "bleeding" sensation if I listen to out of tune music long enough.
However, since I listen to so much music and tune my violin to A 440Hz every time I play, my ear knows when something is off even by a degree or two when listening to some European orchestras. And I think every musician hates out of tune music :)
There is a really cool phenomenon with some musicians who play instruments with a one to one correspondence between a pitch and feeling + fingering (so woodwinds, and sort of brass) that have played long tones for so long that they have internalized the "feeling" of a note and can (with a small delay) seem like they have absolute pitch. Really cool stuff. A youtuber called Saxologic dubbed this ability "Real Pitch". Really interesting video showing this in action: https://www.youtube.com/watch?v=x4zo6POThHc
> And I think every musician hates out of tune music :)
The notion of “out of tune” is different for people with and without absolute pitch. Someone with absolute pitch can hear something as “out of tune” just because it uses A=432 instead of A=440, whereas someone without absolute pitch will hear it as in tune. That is, more or less, THE characteristic difference between having absolute pitch and not having absolute pitch.
I don’t have absolute pitch. I’ll hear a guitar as out of tune if it is not tuned to itself. Like, if one string is flat relative to the others. However, if you tune a guitar to standard tuning in A=432, that sounds “in tune” to me. I think I have a decent sense of tuning—you can tune to equal temperament, and you can tune to just intonation, and I can tell the difference between the two. But I cannot tell the difference between A=440 and A=432.
The difference between 440 and 442 is exceptionally small, I’d be surprised if you could hear the difference in an A/B test.
Singers also get "real pitch," I think, and in general, when you know the sound of an instrument's registers really well, it can be a hack for professionals to turn their relative pitch into "perfect pitch."
Also, FWIW most professional musicians I know can't tell whether their A is sharp or flat by a few cents (eg the difference between 440 and 442), but they can tell interval size immediately. The interval sizing tends to determine "out of tune" rather than the frequency of the A.