I’m not sure it has much to do with being progressive, we’re a fairly conventional heterosexual couple.
Dividing up jobs or parenting roles according to gender is not always practical. My partner just so happens to be better and feeding and getting our daughter to sleep. I’m better at playing with her and encouraging her to take on challenges. He decided early on that he would be an active parent, anyone can do that whether they’re male, female or non-binary. Our roles are constantly shifting, sometimes he is the one she goes to for comfort, sometimes I am.
Sticking to one set of roles, prescribed by a narrow concept of “gender” is too dogmatic to be helpful in the chaos that is new parenthood.