To be counted as a different language, I would say it should be as different as Zhuang language, Tibetan, Uyghur, Manchu, Hmong, etc. People who speak these languages might or might not come from politically controversial regions, but I don't think anyone would consider these languages Chinese for a second.
They share the majority of the syntactic and grammar. Their written form are all the same. Pronunciation is the major difference. This level of unity is established probably since the Qin dynasty.
Regional languages in China have separate writing system when you need to write what is actually spoken.
https://en.wikipedia.org/wiki/Written_Cantonese#Vocabulary
https://en.wikipedia.org/wiki/Fuzhou_dialect#Writing_system
Easiest way to see this difference is watch the news in Cantonese -- it is mostly 书面语 (standard) mandarin but pronounced as Cantonese, whereas day-to-day spoken Cantonese is completely different in structure and vocabulary. What do you think gets written in HK movie scripts? Definitely not standard written mandarin.
Here's what linguists say:
1. From "Visible Speech: The Diverse Oneness of Writing Systems" by John DeFrancis:
"Chinese [...] is an umbrella designation for at least eight present-day varieties of what are usually called "dialects" but, since they are mutually unintelligible, might better be considered parallel to the various languages that make up the Romance group of languages."
2. From "Asia's Orthographic Dilemma" by Wm. C. Hannas:
"some eighty million or more people living in China [...] speak non-Chinese languages written in alphabetic or indigenous systems. [...] If we ignore this inconvenient phenomenon and focus on the speech of China's Han population, we find a collection of at least seven or eight mutually unintelligible varieties that in any other context would be called "languages," but which are "dialects" in China, in part for political reasons and in part because of a problem with the translation of the Chinese term fāngyán. The political motivation for claiming that these distinct varieties constitute a single language is fairly obvious: it is easier to govern a country in which the majority believe they are speaking one "language" (whatever the linguistic reality) composed of several "dialects" instead of several related languages.
[...]
Most linguists familiar with the classification problem acknowledge that the major Chinese varieties differ from each other at least on the order of the different languages of the Romance family.
[..]
We have seen that the Chinese languages differ not just in pronunciation but also in vocabulary and grammar, and that these differences are realized through unique morphemes (or unique uses of shared morphemes) for which characters do not exist at all, do not exist in Mandarin, or are used with different meanings and functions. Consequently, character texts in Cantonese and (where available) in Taiwanese are largely unintelligible to Mandarin readers. Many characters are completely unfamiliar; others are recognizable but make no sense in context. This occurs where conventions exist for writing the non-Mandarin variety in characters. Actually, most of these languages have no established writing system and hence lack even the possibility of being understood by readers of other varieties.
I mean, 90%+ of Chinese people were taught and speak Standard Mandarin anyway. Language is not a reason for separatism today.
and the possibility that Catalonia might break away from Spain: https://www.theguardian.com/world/2016/jan/10/catalan-indepe...
To be consistent with the linguistic facts, one should speak of the Chinese languages. You could also consistently speak of a Chinese language with dialects, and then also consider Romanian, French, Spanish, Portuguese different dialects of the Romance language; but that would redefine the terms from how they're currently commonly understood.
And by politics, I think one really means culture. It is the need of communicating with each other on a daily basis forges a language.
Well, I was mostly commenting on the traditional Chinese. Traditionally most population are illiterate so there is little problem having disconnected spoken language and written language. With the modernization and majority of population becoming literate, there is a unification between spoken language and written language. That has updated both Chinese spoken language and written language to a common form -- dialects are becoming merely a different pronunciation form. Today, with schools mandate speaking of mandarin, dialects (the spoken languages) are on the way out.
This process take place in both the main land and Hong Kong and Taiwan. But due to the isolation, they took slightly different form. That is how to a foreigner's view, Chinese dialects appears to be different languages. This is not fundamentally different from between French and Spanish, only the extent of time differs. With only decades, the Chinese in Hong Kong and main land, e.g., are still viewed by most Chinese as the same language.