Thank you for pointing out the wider context for this debate, you beat me to it. The level of hypocrisy on view in Brazil regarding this issue is breathtaking: implicit acceptance of what amounts to genocide on the one hand, while prosecuting its victims on the other. Given the attitude that Brazil has had historically toward its indigenous population, one would think they would be _encouraging_ infanticide -- it saves mining and lumber companies the cost of ammunition to shoot folks, after all.
The best option here would be to employ applied anthropologists in partnership with anthropologically-aware medical practitioners and demonstrate that disabled children can be cared for, in ways that are culturally compatible with local belief systems. However, this would need to be part of a multi-pronged campaign to recognize the equality and autonomy of native peoples, things which so-called "civilized" populations seem incapable of grasping.
This isn't an either/or issue; "culture" should not be misunderstood as some sort of monolithic edifice that you either accept or reject. There's room for debate and compromise on everything, and the dissent reported within tribes regarding infanticide is emblematic of this. As long as medical practices are presented in ways that respect local communities, it is surprising how well partnerships can be forged between "Western" and indigenous customs. These cultures don't have to "stop," and its clear from the text that not every member of these communities agrees with the practice of infanticide. Approach people with respect, provide information in a manner that fits into their perspective of the world rather than imposing one's own, and work together to find a compromise position that doesn't require killing children. Change is a basic ingredient in all cultural systems. Easy? Of course not, but it can be done.
And to those explicitly or implicitly stating that Amazonia peoples are cruel, barbaric, inhumane, and don't deserve to exist because of the way disabled children are treated, as an American I can point to the way in which my own culture allows children to suffer and die of malnutrition or poor health. Heck, look at how much Michigan's state government cared about children in its territory drinking leaded tapwater. At least the tribespeople described in the article give "inconvenient" children a relatively quick death, rather than letting them linger with life-long brain damage and other maladies as we do here [1].
[1] Hyperbolic Swiftian analogy. Author does not endorse killing people in general, let alone killing children, okay?