Just intonation tuning of chords (but not melodies) is the ideal in barbershop music. Barbershop music also uses harmonic sevenths, which are not found in standard 12EDO equal temperament. I've never heard of anybody calling barbershop "strange" or "disturbing".

I don't think anybody is likely to call a perfect fifth or third those things either. You can easily check using the "Generate, Tone..." feature in Audacity. I recommend using a sawtooth wave, which contains prominent high harmonics that make it easy to hear subtle difference in tuning. The worst criticism I'd make of perfect just intonation is that it can sound boring, for the reason the GP post suggests.