Sure, but it should be pointed out that many nationalist ideas propagated by the republican revolutionaries were actually imported from Japan, including the minzu concept.
The "split up" as in from the 5 ethnic groups in Qing and early republican China (5 races under one union) to 56 in the PRC. The Hui was historically used to refer to Muslim Turkic people in Western China. You know this.
The definition of who is Han changed from early republican China to the PRC and a group that identified themselves as Han got excluded in the PRC. But for the life of me, I cannot recall which one right now. The distinction was supposed to be based on the Stalinist definition of nationality or ethnic group, but it was rather liberally applied.According to this definition, a nationality was supposed to have the four following characteristics in common: language, territory, economic life, and mindset or culture. By the 1950s, most Manchus would have hardly qualified as a separate ethnic group according to the above. Very few were still able to speak or read the Manchu language, nor where they geographically concentrated in any one area.
That was in no small degree due to the rampant ethnic discrimination against banner people in the Republic of China. A large number of Bannermen adopted Han style surnames in the early republican period to escape discrimination. They even stopped observing their Manchu customs and stopped wearing their traditional dresses. Because a large number of Manchu men fell into destitute poverty and were unable to attract marriageable partners many Manchu women ended up marrying Han men. The Nationalist actually went much further than the early republicans: they denied that Manchus constituted a separate ethnic group and asserted that China was ethnically homogeneous. Sun Yat-Sen's Nationalism was only to be achieved by the creation of a new Chinese ethnic group (Zhonghua minzu). Modeled on American ethnicity, this Chinese ethnicity was to take the Han people (Hanzu) as the core and have the other four peoples (Manchus, Mongols, Muslims and Tibetans) all assimilate to them. For example this is why Lao She did not acknowledge his Manchu ancestry during that time. In the census taken in 1953, just 2.5 million people identified as Manchu, which is half the estimated banner people in late Qing.
You are hilariously off base.
The "5 ethnic groups" under Qing referred to the five most politically important ethnic groups under Qing rule: Han, Manchu, Mongol, Hui, and Tibetan. It never meant there were only five ethnic groups.
The Hui, in particular, was a general term for Muslims. It encompassed ethnic groups from Yunnan to Xinjiang. Under the PRC, Chinese Muslims were separated into the current nationalities. The modern Hui is basically composed of Han Chinese who are also Muslims.
Now its true that things were screwed up under the ROC, but you need to keep in mind that the ROC never controlled the entirety of China. Their rule over many of the minorities were only theoretical. The PRC was the first stable political entity after the fall of Qing to control the entirety of China, minus outer Mongolia and Taiwan if you want to quibble.
So what that means is the ROC classifications are worthless because they hardly had any dealing with those ethnic groups they blithely classified. It was only the PRC that went to do the whole administrative work to arrive at the current 56 nationalities classification.