Instead of just arguing over if the POD is right, I'm going to take a shot at it to get the ball rolling - correct anything you want, I'm just spitballing here.
1855 - Frederick Townsend Ward, having enlisted in the French Army dies of dysentry in the Crimean War. He never makes it to Shanghai and without him the Ever Victorious Army is not ever victorious.
1860 - Taipings approach Shanghai, defeating the Shanghai Foreign Arms Corps financed by the merchant interests. But these were businessmen, and were always ready to deal. The Taipings wanted access to a port, and the Manchus to lose Shanghai. A group of merchants met with Taiping commanders, and worked out the Shanghai Concordat. The merchants financed the overthrow of the Manchus in Shanghai, and declared it an open port. The Taipings would have full access. On paper Shanghai was governed by a council of merchants (both European and Chinese), but in effect was controlled by the British Consul.
1863 - The war along the Yangtze is hurting trade, badly. In order to end the war the powers, led by Britain and France, recognize the Taiping government in southern China. They demand the Manchus stop the war, and march on Peking to enforce peace. The Emperor is killed in the battle as the Summer Palae burns. The Empire descends into chaos.
1863-1866 - As the Manchu Empire burns the powers scramble for the choicest parts of China. The British take Canton, the Pearl River delta and Formosa. The French take Hainan Island and parts of Fujian province.
1863-1890 - Taiping flourishes with free trade down the Yangtze and good relations with their fellow "Christians" - their religion is taught extensively in their country, and is linked to success and prestige in government and business.
1865 - Yakub Beg seizes and expands muslim Kashgaria
To 1895 The northern "Chinese Empire" is wracked by civil war, between various Manchu claimants and Han usurpers. Parts of the south are industralising and being better educated under British and French rule. The continued civil war in the north is seen as a opportunity for the other powers, notabaly Germany, Russia and Japan.
1895 to 1905 - Various wars between China and Germany, Russia and Japan. German and Russia areas meet at Tientsin.
1914 - The First World War breaks out and German and Russia troops fight in northern China, both use thousands of native troops.
1915 - Amur Massacre German led Han Chinese troops massacre 22,000 Manchurians on the Amur who were under Russian command.
1917 - Treaty of Brest-Listovsk - Russia gives up parts of Manchuria under German occupation - retains Outer and Inner Mongolia and territory along the Amur (more or less today's Heilongjiang province).
1918 - German home front collapses - Army in Northern China is undefeated and refuses to abide by the Treaty of Versailles giving Germany's Chinese colonies to Japan and France.
1924 - Mongolia and Red Manchuria are declared SSRs of the USSR.
So by 1920 we have:
1.
Taiping Heavenly Kingdom - South of the Yangtze excluding Fujian and Guangdong provinces. Very different from rest of China due to official religion, language not being mandarin, and good relations with British and French - richer too due to open trade on the Yangtze.
2.
Emirate of Kashgaria - Muslim state, limited Han immigration ruled by Tajik dynasty - sees itself as part of the Central Asian dynamic - much more interested in what is happening in Afghanistan than what is happening on the Pacific coast.
4.
Crown Colony of Canton and Formosa - British China - official languages are English and Cantonese. Mandarin is discouraged, what industrialisation that has happened in China has happened there. Education levels are higher as well. The native inhabitants look down on northerners as of a decidely lower class.
5.
Fujian - French Colony. Better education, fought Germans in First World War - closely tied to Shanghai economically.
6.
Hainan Island - Integrated in French Indo-China - Viet and Cambodians are imported to increase agricultural output.
7.
Grand Duchy of Shandong - German ruled coast China. You though the Freikorps was trouble. These guys have an economy, and a population that feels better off than under the Japanese or the Manchus.
8.
Japanese China - The Liaodong Peninsula integrated with Japanese Korea.
9.
The Empire of China - Rump state riven by civil war, hampered by lack of economy, access to the sea and education. The people feel little connection with the Emperor (whomever it is this month) and are a little jealous of the better living standards elsewhere.
10.
Red China - Mongolia SSR and Manchurian SSR. Soviet Republics under Moscow's thumb. All education is in Russian, religion is banned. The gulags in Mongolia become espescially notorious.
11.
Free City of Shanghai - Economic centre of China. People are flocking there from the interior. Very cosmopolitan.
12.
Tibet - of course
Rough map is attached.