"Anything Goes" is a play from a number of talents including Cole Porter and P. G. Wodehouse. At the time it was written it was intended to be contemporary, so the 1930's a time of post-stock market crash recovery, a time when the US to UK boat journey was an extravagant party.
The book has been revised and updated, to attempt to adapt to a modern day audience that would expect female and/or Chinese characters to have equal personhood.
The program at Arena Stage's production mentions that they address things in classic musicals with a three pronged approach casting (Corbin Bleu is the most recognizable cast member and is biracial, there were also other visible African American, and Asian American (not just the two Chinese cast members) cast members), direction, and book changes (with permission of the writers).
"Anything Goes" is a farce, as you might expect with Wodehouse on the original team. No one is telling the truth, and of course after the first scene, they are all on the boat together. This version allowed the two Chines characters, John and Luke, to demonstrate early that they were performing their own con, which helps a lot in making them characters rather than caricatures. It does still include the song "The Gypsy in Me". That song is one of the few that isn't instantly recognizable to audiences and, probably because using ethnicity as an excuse for bad behavior is not great.
The production is wonderful, and the cast great. Corbin Bleu as Billy and Soara-Jaye Ross as Reno are especially notable. The cast also did a great job of being funny by being serious, even as they broke the fourth wall in one number and teased an audience member and stole the conductor's baton. Also Reno goes through more costumes than anyone and all of them were delightful.