I'm also in a social group where men pulling their weight domestically is normalised. Any man whose words or actions suggest that housework is women's work finds those kind of jokes fall flat, and gets snide comments when he's not there from both the other men and the women. Equal partnerships are also nornalised - DH and I are child-free and this dynamic is obvious whenever we visit our parent friends. There's no such thing as "the women cook and tidy up while the men go and sit and talk about politics" because the women will most likely do the latter as well, with or without the men.
Indeed there isn't actually a division between the "female social groups" and "male social groups". If someone's hosting a gathering, than any given group of my friends in the kitchen with the food, or in the garden chatting about current affairs, or looking after the kids, will probably contain both men and women. I can't imagine being in a social group where gender segregation by activity was even a thing.
How to replicate it? Well none of the above was an accident. I grew up in a household where traditional gender roles were encouraged and wanted none of it for myself. As a young adult I gravitated towards like-minded people and the ones who became my closest friends are the ones who broadly shared my views. And we talked about it all in our 20s, we all bonded over rejecting traditional gender roles! (And there are plenty of LGBT people in our social group, it's not really heteronormative in any way.)
Social groups where women went on girls' nights and had to live up to some weird trad ideal of femininity/where men went on lads' nights and had to live up to a trad ideal of masculinity were just not for me. I found those people boring and I avoided them.