Obviously what ICE is doing is awful, and vasectomies would in some ways be an improvement (although big doubt that they want a reversible birth control procedure). But critiquing what is clearly steps of a genocidal program on whether or not is patriarchal seems to miss the point.
It's a tacky way to phrase it, and you're right that the main problem is that it's, y'know, genocidal.
But I don't think it's totally wrong to point out the patriarchical angle. A big part of the right-wing worldview comes down to "Women are baby-making machines to be owned and controlled by the men in my ingroup (often defined by culture, religion, race, sometimes class), and society should be structured in such a way that the birthrate of babies is managed, and preferably maximized, by and for that ingroup AT ALL COSTS, including the sacrifice of personal freedoms and quality of life." So I think there is value in pointing out the patriarchical nature of what they're doing, insofar as it interacts with the genocidal nature of it.
Yeah, I think this is the way to look at it that makes the most sense. It's horrifying no matter how you look at it, but their choice of victim is telling.