Breakfast at Tiffany's was made at a time when Hollywood wasn't all that pressed to cast roles according to the race of the characters. Many films from the era still featured all-white casts even if the script dictated that they're not actually playing a Caucasian.
Which brings us to Tiffany's Mr. Yunioshi. Is his yellowface makeup and transcendent stereotypical performance off-putting? Well, yes, but Yunioshi's contribution to this classic film is indisputable so...wait, what's that? This entire movie could play out with the exact same beats without Mr. Yunioshi the eccentric Asian neighbor? Oh.