I would say the "possible" (I'm honestly not quite sure how widespread it is) sterilization that might've produced a massive drop in birth rate is one of them

I totally put off responding to this but remembered it and wanted to mention to you that IUDs would be an incredibly stupid way to conduct a "sterilization" campaign, since it's meant to be a very temporary procedure and is thereby totally reversible. Historically we have seen what actual sterilization campaigns tend to look like (chemical castration of Ethiopians in Israel, hysterectomies on migrants in the US) and they are not the sort of thing where the victim could hypothetically go to anyone with training as a gynocologist and have it safely reversed in literally a few minutes.

It seems much more likely when one sees a large uptick in IUD insertions in a historically impoverished area where women have comparatively less autonomy to be things other than homemakers that perhaps this is something women are doing voluntarily as a product of recent development rather than due to compulsion.

And the other is the too broad institutionalization of people based on their activities, I know they're not just putting people in these institutions against their will because they are muslim, there has to be other criteria, but I find it hard to believe that everyone (or maybe even most) who passes through them actually was, or had a probability of becoming, a terrorist.

I think you know that this is a really nebulous claim, but it's worth noting that these people weren't taken to Guantanamo Bay or even to a "prison" in a recognizable sense of the word. A segment of them were imprisoned in the literal sense of the word (though with freedom to return on weekends and keep contact with the outside world), but what they were doing wasn't breaking rocks in a quarry, it was receiving education and vocational training. For someone who was at-risk in part due to poverty or social insularity, these are not terrible things to spend a year on. Granted, that doesn't justify just rounding up people willy-nilly, but it makes "concerns" about not-at-risk people likewise require a little more substantiation.