Meh. I support some forms of eugenics as at least interesting ideas (not this one in particular, or in general any that involve force and non-consent). Saying "This was supported by Hitler!" or "This is eugenics!" is lazy arguing. Things are not wrong because of who else liked them or because of which particular word you choose to apply to it. Things are wrong because of reasons like being forced on unwilling participants on flimsy justification.
Call me crazy, but focusing on shitty arguments when the good ones are plentiful bothers me.
An idea that was supported by Hitler isn't necessarily wrong because it was supported by Hitler, last I heard the Autobahns were a rather decent bit of national infrastructure.
However if someone is deciding that the right to reproduce is a privilege granted by the state based on the worthiness or lack thereof of an individual then I think the comparison is apt. Nazi Germany's Eugenics policy was based on the notion that some
life was unworthy of life and that only "worthy" people should be allowed to reproduce as opposed to say, criminals, dissidents or the disabled. This wasn't a bad thing because it happened under a regime led by Hugo-Boss wearing Nazis, it was a bad thing because it caused an injustice to occur.
Cat's argument has key things in common with those of the Nazis and also previous generations of American Eugenicists that inspired the Nazis in saying that reproduction is a privilege that should be granted by society rather than a fundamental human right and that that privilege should be granted to people based on the value they give to society. The justification for the Eugenics being proposed here is not based on anything genetic but rather a subjective moral value that can be placed on certain classes of people.
Cat's rationale differs from the Nazis in that they did not want undesirable elements reproducing whereas Cat seems to be motivated by the welfare of their as yet unborn children and the effect they might have on society at large. The overall effect is the same, you make a value judgement about someone's worth and then impose a permanent physiological change based on that assessment.
My problem with this position is that once you allow the state to remove peoples ability to reproduce then not only are you violating the fundamental human rights of those who are subjectively considered to be "unworthy" you are also allowing the state to make irreversible decisions about peoples lives that might later be found to be unwarranted or mistaken. Any complications or injuries arising from botched procedures can likewise not be undone.
Granted, imprisonment can also be found to be unwarranted or mistaken but forced sterilisation is a different class of punishment, more like capital punishment in that it cannot be reversed or undone. A prison sentence can be cut short, a sterilisation cannot. Compensation doesn't make up for years in prison, equally it doesn't make up for losing your ability to reproduce.
The women in this story were not uniformly imprisoned for culpable offences like rape or murder, and an effective permanent sentence imposed on them would be unjust in most cases. I'd question whether permanently altering someone's physiology because of their perceived worth or because of what they might do is useful to anybody. It will hurt some people, and there's no good reason to believe that it'll help anyone.