Breastfeeding is an issue that affects mothers and their children — there is no need for gender neutral language.
The erasure of women and mothers from breastfeeding support has been a slow but steady creep over the past couple of years. Both internally and externally, pressure on peer and professional breastfeeding organizations to update language and imagery in order to centre the experience of individuals and families who identify as transgender and non-binary has increased. “Mother” should become “lactating parent,” “breastfeeding” should become “chestfeeding” or “human milk feeding,” and so on. Rather than expand the terminology to “mothers and _____,” the demands have typically been to eliminate references to women or female bodies in order to demonstrate respect and care. This has also been accompanied by an increasing number of attempts to normalize induced lactation in fathers and trans-identifying males, with total disregard for the impact these interventions have on mothers and babies (including the lack of evidence regarding male milk composition or the safety of the accompanying drug regimens for a baby consuming the resulting milk).
Source: Why are women are being erased from breastfeeding advocacy?