Gilbert and Sullivan's The Mikado, or the Town of Titi-Pu is still one of my favorite things in all the world--for pure, human joy, it's hard to think of anything that comes close to the end of Act I. That said, there are moments that make me, child of the late 20th century, really very uncomfortable.
So, as you should know, Mikado is obviously about England, not Japan, but all the same, it is set in Japan and keeps making crude, stereotyped reminders of its setting, as seen from the haughty position of Victorian England. The racist caricatures are genuinely offensive, and the cringes they induce do detract from the modern listener's enjoyment. There's a fair bit of that in G&S--just about all of Princess Ida, which mocks the idea of educating women, for example. So what to do?
Some say, don't perform it. That's a non-starter. The music and words, when not tainted by offensive antique attitudes, are priceless.
Some take the approach of ignoring it; you can go to you tube and watch a production by the English National Opera, with Eric Idle as the Lord High Executioner, which sets the events in a 1920's English seaside resort. Fine as far as it goes, but the lyrics are still there, and it's kind of disorienting to have people singing that they are "gentlemen of Japan" when they are clearly gentlemen of Brixton or Leicester.
I would be interested to see this, New production. It keeps things as G&S intended; but, it frames it by Gilbert getting bonked into delirium, and having the whole production be his personal dream. A nice way to insulate the audience, and make it clear that the racism really truly belongs to Gilbert, not us.
Perhaps the way is what opera buffs call "regietheater," where the director takes a stiff dose of LSD before deciding on the staging. So, set it in an insane asylum in Nazi Germany, or make the characters all rats in a behavioral scientist's laboratory. I don't know what's best, or how to dissolve away the stuff that really is offensive. I do know that the music and almost all of the words give me so much joy, and that the world would be a much darker place without them. Oh willow, tit-willow, tit-willow!