The problem is, this practice has already taken hold.
I've recently had a baby and see this frequently. I've already mentioned a few times on this board that my antenatal class replaced the words 'mum' and 'mother' with 'birthing parent' on their literature when I was part way through the course.
Some (thankfully not all) breastfeeding cafés now advertise their services as being for 'breastfeeding and chestfeeding parents'.
Even 'breastfeeding parents' irritates me. Only one sort of parent breastfeeds. Mothers.
Fathers, partners etc. do not breastfeed.
American websites are entirely hopeless - I've lost count of the times I've read an otherwise sensible article about birth or breastfeeding from a reputable US organisation, only to find that the words 'woman' and 'mother' have been carefully removed from the text. Whenever I check, there is usually some indication that the article was updated in 2020 or 2021. UK websites are better, but for how long?
I'm glad Stonewall has changed its policy, but unfortunately I think some damage has already been done.