They also expect that in the case of childcare, both parents are utilised
This is the key, all employees, not just parents, have a right to flexible working and fathers being expected, by their employer, their partner and society, to do half of pick ups, drop offs, sick days etc, and a decent chunk of parental leave, not just the minimum 2 weeks, but say 3 months. Also reduce presenteeism culture and travel for the sake of it. Hopefully the latter will be a silver lining that emerges from the great black cloud that is COVID-19.
So employers don't see it as an issue when employing women and you are less likely to get into the situation where the mother decides she has no choice but to give up work because she can't make all the running around and covering sick days work as well as her job so gets a reputation for not being committed while fathers get to concentrate solely on work and put the hours in, so they get ahead and if it comes to the stage where the family can't cope, it's almost always the woman who decides to give up work because the children's father earns more, because he's not been the one who's damaged his career due to being a parent.
Civil service - extremely flexible (but only in the right department and role)
Definitely agree with this caveat. I'm a civil servant but in a department that offers a commercial service. There is flexibility, but it does also requires long days (12-14 hours) at least a once or twice a month (in normal times anyway) and quite a bit of travel, depending on what projects we are undertaking and certainly within the first few years of the role, due to lots of training courses and spending time working at our various different sites. Definitely cannot be done as regular set hours and being at home every night, so would need a supportive partner for childcare purposes.
Plus anyone working on COVID-19 response or to a lesser degree, Brexit could be working on a 24/7 rota and extended hours above the normal 37.5 pw.