There's another story here.

The Uighurs and Hui are not the only people who are Muslim. The Chinese govt attempts to frame all people based on ethnicity and then assign religions to each group and identify religious groups by their ethnicities thereafter.

However, there are millions of Han who are Muslim. Moreover, the actual number of Muslims in China is far greater than the Chinese govt admits. The govts claims Muslims compose only 50 million. However, they calculate this by identifying Hui and Uighur population numbers and claiming they represent the number of Muslims. However, there are estimates of 50 to 100 million Han and Manchu Muslims who go unidentified.

As well, the 50 million number was based on 1950/60s population censuses. So this official number is skewed several ways.

In Beijing, there are mosques, halal restaurants and markets, and Muslim names everywhere. The Chinese govt is forced to accept Muslims because they are part of China and have been for centuries, but they are intentionally trying to suppress the official presence of Islam because the Communist Party is the reserve for the elites.

Aren't the Hui essentially just Han Chinese who happen to be Muslim, but were, as you noted, defined as an ethnicity in order to get around the ideological problems involved in recognizing a religion?

Why wouldn't Han Chinese muslims just be counted as Hui? Or are they under registered?