What inspiring and practical examples!
Maybe a commitment to impact causes EA parents to cooperate at maximizing it, which means optimally distributing the parenting workload whatever society thinks. In EA with lots of conferences and hardworking impactful women, it makes sense that the man's op cost is often lower. Elsewhere couples cooperate to maximize income, but men tend to have higher earning potential so maybe the woman would often do more childcare anyway.
My sense is that parenting falls on the woman due not only to gender norms, but also higher average interest in childcare and other confounders-- so I wonder how much is caused by other effects like EAs leaning liberal, questioning social expectations in general, or EA dads somehow being more keen on parenting. Also it's unclear if EA men even contribute more than non-EA men.
I'm reminded a bit of the gender equality paradox where in the USSR, and maybe also countries with restrictive gender roles [1] there are higher rates of women in STEM and other male-dominated fields. The idea is that in liberal societies, there would be a disparity due to difference in interest, and some kinds of external factor can reduce disparities on net-- in the Soviet case because equality was enforced by the state, in other cases if there is economic interest or a lack of Western stereotypes. So EA mindset is maybe one of these external factors-- not to imply it's like Soviet central planning or anything.
[1] the research seems disputed here

Thanks for thinking to write this, Julia! I appreciate reading how other couples navigate this and can think of a number of other strong examples.
For my part: my beloved career at GiveWell is enabled by my husband, who is a stay-at-home-dad. He also brought our kid(s) along on my work trips (2-4 per year) for over two years when our baby-feeding configuration made it impossible for me to travel without them.