As I understand it, it is the case that Chinese in different areas have different pronunciation to the extent of being mutually incomprehensible, but share one common written language.

Some suggest this is equally true with English, although here is is often the dialect words that block understanding. A strong accent will however often prove difficult, especially for southerners.

A standard pronunciation of Chinese characters was used for many years in the west, but it had many flaws so a better one was introduced and is now in international use. How this is based on one particular, or a blend of many, regional variations I do not know. I suspect it is based on Mandarin as spoken in the capital, as is usual in these matters and independent of the political system in operation.