I've studied feminism for quite a bit of time now and I struggle to find any actual evidence of the 'blind', work-obsessed feminism James (and his subeditor) refer to.
In the 1970s, the supposed decade of 'loony' feminism, feminism was about sharing childcare responsibilities, not only with men but with other women. Children were seen as the future of an equal, nonmaterialistic society in which women would not be seen as worthless, invisible domestic labourers. That was the message, not 'go to work and be a MAN my girl'. As other posters have rightly said, that message comes from Thatcherism and neoconservatism. The message now is that only wealth creation counts. If you're at home, you have to be creating little wealth creators. And some commentators think that would be better than making it yourself. Either way, women are still indelibly associated with childcare and all the emotional triggers around it which is why women actually feel more inclined to stay at home/worry themselves sick about childcare. If people and society in general really believed this was not a 'woman's problem' headlines like this one would not get written at all.
I find myself doing a PhD (for miserable grant money, now run out) and due to Dh's higher earnings, paying for a nanny whom I constantly flap about (she just doesn't do what I WOULD do if I were at home, etc...). I pulled him out of his nursery because I felt he just wasn't getting affectionate care & couldn't stand the guilt. DH just didn't feel this to the same extent although he is a very involved parent as far as he can be. No one at his work ever asks him about his childcare 'responsibilities'; his job is constructed as if he simply doesn't have any. He gets praised as 'wonderful' for 'allowing' me to study and paying for childcare which I couldn't otherwise afford. Society doesn't see us as equally responsible for our child and even I, the ranty feminist, have internalised that message to some degree.
It will take generations to get rid of this sort of gender typing. I just wish we lived in a world where little boys could push toy prams and say they want to be nurses or primary school teachers without being laughed at, because we are a really long way from encouraging men to consider themselves equally responsible for childrearing.