Even in very liberal sf bay, there are not so subtle exclusionary biases against fathers as primary caregivers which I have experienced on parental leave. In passing in the grocery store, there are nods and acknowledgments, but in classes, the local "mothers group", and the support infrastructure for new parents, there is a lot of non-inclusive language. As a most privileged person, I take this all as a very gentle lesson in what it is like to be not in a position of privilege, but I do think it contributes to men opting out of primary caregiving. Also, breast feeding.
Choosing to prioritize children over career reasonably impacts career trajectory. I'd prefer if we had more gender oblivious parental policies and expectations instead of reinforcing gender essentialism through overly targeted programs.