If I've understood it correctly, China isn't persecuting Muslims, but Uyghurs, and their main justification for it is the East Turkestan independence movement. There are plenty of Muslims in other parts of China living normal lives.
Chinese government statistics show that from 2015 to 2018, birth rates in the mostly Uyghur regions of Hotan and Kashgar plunged by more than 60%.
I assume you're referring to this part of your link:
> In March 2017, Salamet Memetimin, an ethnic Uyghur and the Communist Party Secretary for Chaka township's Bekchan village in Qira County, Hotan Prefecture, was relieved of her duties for taking her nikah marriage vows at her home. In interviews with Radio Free Asia in 2020, residents and officials of Shufu County (Kona Sheher), Kashgar Prefecture (Kashi) stated that it was no longer possible to perform traditional Uyghur nikah marriage rites in the county.
Such a policy against nikah marriages would also affect other Muslims, not just Uyghurs.
> Combined with some forced sterilization and forced contraception and you get a “mild” form of genocide that destroys a people without producing mass graves.
Similarly, forced sterilization has been part of government restrictions on reproduction for decades, and although the limit has been raised with the abandonment of the one-child policy, there's still a limit. So it doesn't just affect all non-Uyghur Muslims in China as well, but actually everyone. https://www.nytimes.com/2017/01/07/world/asia/after-one-chil...
In the New York Times article I linked above, it is mentioned that "From 1980 to 2014, according to official statistics, 324 million Chinese women were fitted with IUDs. And 107 million underwent tubal ligations or, as is commonly said, got their “tubes tied.”" Most of those cannot have been Uyghur women, since those figures vastly exceed the total Uyghur population.
So other parts of China simply suffered their sterilization campaigns much earlier. Birth rates in Xinjiang only dropped slightly from 17.57 per thousand in 2000 to 15.88 in 2017, but then to 10.69 in 2018 and further to 8.14 in 2019: https://data.stats.gov.cn/easyquery.htm?cn=E0103&zb=A0302&re... , which is a fast drop; but in Beijing, the maximum birth rate over the past 20 years was 9.32 in 2016, and their 2019 birth rate was still below Xinjiang's at 8.12: https://data.stats.gov.cn/easyquery.htm?cn=E0103&zb=A0302&re...
In terms of IUD rates. 324 million IUD’s over 34 years vs a current population of 1.4 billion don’t on their own get 60% drop in birth rates. Further, it isn’t like Xinjinang was completely outside of the national trends and suddenly caught up, this is clearly deliberate genocide based on openly available data.
Yes, it's harder to avoid the government's wrath if you live right under their eyes in the capital, so national policies are more likely to be enforced in Beijing than elsewhere.
> In terms of IUD rates. 324 million IUD’s over 34 years vs a current population of 1.4 billion don’t on their own get 60% drop in birth rates.
Did you do the math on that? 1.4 billion population total corresponds to roughly 700 million women; adding 324 million IUDs and 107 million tubal ligations amounts to 431 million sterilizations, about 62% of all Chinese women.
Of course it's not just the sterilizations that cause a drop in birth rates, but also having to pay a fine per "superfluous" child, not qualifying for government benefits, the rising cost of living making raising a child more expensive etc. It's no wonder that many women would choose to have no or fewer children under these circumstances, especially if they know other women who can tell them exactly what it's like.
> Further, it isn’t like Xinjinang was completely outside of the national trends and suddenly caught up,
I do think they were outside national trends in terms of percentage of women sterilized and "caught up" by sterilizing women en masse even when they gave birth years ago; while those sterilizations would have happened routinely after childbirth in Beijing.
I guess we'll see whether birth rates in Xinjiang will continue to drop below even the level of Beijing, stagnate at the current level or bounce back slightly once the figures for 2020 are published (but then there's the pandemic as a confounder...)