Mikado is problematic, but viewed in the context of the 1880s it's clearly gently mocking cultural appropriation by the English middle classes. Which is why Gilbert was so careful to get costume, movement, etc exactly right to highlight the absurdity of an English social system in Feudal Japan. Apparently Japan has a revival production every so often and they get the point much better than modern western audiences.

Now Princess Ida, incredible, Sullivan's second best score after Yeomen, but super problematic.