Killing babies is taboo for us, but not for them
The easiest way to humanize something is to show why it's done. Explain, through expository, the physical and cultural circumstances that lead a character to kill an infant. This applies to infanticide, fratricide, genocide, regicide, and every other kind of -cide there is. While modern readers may be horrified by the result (perhaps this is the intent), if the expository is sufficiently persuasive, the reader should as least understand why the character takes that action even if the reader doesn't agree it 'the right thing to do'.
If the babies are being killed because of resource constraints, then describe in as vivid detail as possible those constraints. If they are killed because of cultural traditions/misunderstandings then describe that culture.
The fundamental problem in describing this is that modern first world societies can "afford" to pay the costs of physically/mentally disabled children and adults. There are much stronger limitations on what can be done to people in the out-group. Readers coming from modern societies just don't have a good handle on what really deep privation looks like, or the feelings of abject fear at the unfamiliar. It is difficult for them to relate to circumstances where killing a baby (directly or through inaction) is the 'right thing to do'.
Many human societies throughout history have practiced infanticide, for many different reasons. A quick reading through the Infanticide Wikipedia entries shows that it's a very old practice.
There is a fine line to walk on this topic. Advocating infanticide is different than describing it. The author will need to be very careful to describe the practice of infanticide and the reasoning of those who do it, without condoning that behavior.
You want the reader to say, "Oh, I get why you would do that. It's horrific in the extreme but I get why you do it."