Work-family policies strongly affected women’s choices, but not men’s.

women disproportionately benefit from the policies since they are expected to be caregivers, while men are stigmatized for using them.

So, work-family policies strongly affected men's choices too, by denying them a choice. Poor writing or worse logic.

Yet those who had children had different attitudes. Of millennial men who were already fathers, 53 percent said it was better for mothers and fathers to take on traditional roles.

I would argue that's a bad statistic. The set of 'MIllenial men who are already fathers' is likely to be composed of people who got pregant and married young, probably with strong conservative religious influence. So this group is predisposed to be more conservative than the general population of 'Millenial Men' already.