To make matters worse, or maybe better, most non keyboard instruments have no sensible temperament whatsoever. Even fretted instruments are a compromise.
Most non keyboard instruments have ways to adjust the pitch slightly per interval while playing, allowing experienced players to play all intervals perfectly.
Yes. I played flute as a kid, and I remember C-sharp in particular as being troublesome. Today I play double bass, and of course intonation is a significant factor in technique. Also, good players will push the notes up and down for effect.