> (Is this why the classic meme of classically-trained performers not getting along with jazz artists? Because the jazz artists won't stay on beat, and this irritates some perfect-pitch-like "out of tune" feeling in the classical musician?)
I think you’re getting tempo, pitch and time signature mixed up. Jazz musicians are excellent at staying on tempo. Staying on tempo is so important in jazz that when I was young, we had to earn the right to practice without a metronome. At the highest levels, jazz can be mixed with jazz because the tempo is solid enough.
Jazz though uses some time signatures that are hard to visualize. Once you’ve played them for long enough they become second nature but they’re likely the hardest part of learning to play jazz. Those time signatures are also common in classical music. Getting time signatures mixed up can sound absolutely awful and that’s a hard thing to fix on the fly unless you know the musicians extremely well (though then the odds of playing the wrong time signature are quite low). Learning to improvise is an entirely different can of poisonous snakes but in an ideal setting you wouldn’t start improvising until you can play.
Pitch can be a problem, but it’s easy to hear and correct on the fly.
As for classical and jazz musicians getting along or not, when I grew up the usual transition was classical to jazz. When jazz was first being invented, there were some racial issues between (generally Black) jazzbos and classical heads. But when I was growing up, we were all band geeks and had a lot of mutual respect for each other.
One thing I’ll note though is that music communities (much like software communities) can seem very toxic to outsiders. If you want to get good, you learn to take and give very direct feedback. It’s a problem when you have a very gifted musician playing with beginners, but amongst musicians of the same calibre, it’s a really warm, loving feeling.