I visited beautiful Anglican churches in Bermuda and the Bahamas in shorts, and maybe a baseball cap, no problem. They do like to see Andrew Jackson’s portrait in the donation jar, though. In London, I visited the crown jewels in jacket and tie, and the attendant, somewhat curtly I thought, told me to button my jacket. A friend had the same experience visiting Lenin’s tomb, before the break up of the Soviet Union, the attendant asking him to button up his jacket. I worked with a guy from Hong Kong (Ph.D. in Electrical Engineering from an English university) who was fluent in Cantonese, his first language, and who visited the Great Wall. When he tried to buy post cards the vendor gave him cards in Japanese.
I think they speak Mandarin in that area of China. It's considered the language of emperors over there.