As always, there are physical things, and there are reactions to those things.
The way you respond to those physical things differs from person to person and from group to group.
This story should be better known: Berlioz took a choir from the big city out into a rural area. The choir sang in standard four part harmony and, since this sometime between 1830 and 1850, the music was tonal.* The villagers' response? That the choir members seemed like nice people and all but they couldn't sing in tune.
In tune for those villagers was unisons and octaves only.
I can't think of anything that sounds abnormal to me. When I was in college, I used to have to play scales for my trumpet lessons. I liked to end them with pitches other than the expected one. I did that so much, that C to C# started to sound as "normal" as C to C. At first, for me, it was for shock effect. But once the shock wore off, I was left with simply another sequence. C, D, E, F, G, A, B, C#. C, D, E, F, G, A, B, D.
Perhaps that was one reason it was so easy for me to hear musics by Bartok and Stravinsky and then Carter and Stockhausen and then Mumma and Varese as completely fine and normal.
There is a thing called acoustics. There are frequencies. Different frequencies can sound simultaneously. But how we react to those things puts us right back to that subjective stuff that seems to exercise so many people. Heigh ho.
And it's true that if you halve a vibrating string, you'll get a pitch that's an octave higher. And the unwary have always wanted to make a big deal out of that. But as Berlioz pointed out almost two hundred years ago now, making strings vibrate is not the only way to make sounds. It's not even the only way to make sychronous pitches. Hitting bits of wood or metal can make pitches, too, as can blowing through tubes of various lengths, thicknesses, and materials. And in those cases, there's no simple cutting in half strategem for making an octave.
As for all the wonderful world of the overtone series and such, the tempered scale that our ears have become so accustomed to is itself a strategem that means that everything is always just a little bit out of tune. So much so, that something in just intonation will sound out of tune to most people.