Here's an interesting article on "Topsy Turvy" and its use of "The Mikado." The article goes into great deal about Gilbert and Sullivan's intentions with the opera and seems to get it right. But why question Mike Leigh's use of the opera? It seems obvious to me that it was a crucial time in Gilbert and Sullivan's partnership and that's why he chose it as the subject.
As for the racist aspect, the opera certainly has that in it. But Leigh doesn't hide from that. The movie offers up the musical without comment. He expects his audience to be smart enough to make up their own minds about the musical and its political intentions, aspirations or unintentional messages.
And Leigh makes it explicitly clear in the movie that England at this time was a very racist place, that racism was not only accepted but was considered common sense.
I just don't see the problem. The movie tells the story of how it was. The director obviously loves Gilbert & Sullivan, but he doesn't give them any free passes. I think the director expects you to make up your own mind without any heavy-handed politicizing.