As long as universities continue to avoid taking the lead on making policies about family leave for graduate students and postdocs, it's going to matter what individual professors (PIs) think about such things. So, if you are a graduate student or postdoc who is concerned about work-family issues, presumably you would prefer to work with a professor who has a constructive attitude about such things.
How do you find out in advance which professors have which philosophy?
If you are a graduate student or postdoc who wants to work with a professor who will be accommodating (as much as possible) for "family events", such as the birth or adoption of a child, I don't think you can predict from the gender of the professor what their philosophy about such events will be. Whether an advisor is sympathetic to "family events" that distract their students/postdocs from their Research has nothing to do with gender.
I think that both male and female advisors can be more or less accommodating depending on their personality, life experiences, career stresses, funding situation, and mysterious factors no one can predict. It is not necessarily the case that female advisors will automatically be more "humane" about these situations; similarly, I do not believe (as some do) that female advisors are less understanding, especially if they are the dreaded single, bitter, and old FSP. And ditto for older male professors who don't know what it's like to have a wife with a career and/or who don't respect young male professors who want to spend time with their kids (and spouse). Such people exist, but there is no general rule about gender or generation that will reveal to you someone's likely advising philosophy.
Whether a professor is also a parent also isn't a good indicator of their advising philosophy re. advisees who start families. For example, advisors who are also parents may or may not be sympathetic to their advisees who become parents. In fact, I know some advisor/parents who are less understanding about work/life challenges because they are afflicted with the "I suffered, so you should too" syndrome. I, for one, don't want hear for the nth time the story about an intrepid female colleague (or a male colleague's wife) who went to a conference or taught a class or was back in the lab within minutes of giving birth. (I am exaggerating, but not much.) These are not likely to be people who will understand if someone needs to rebalance their time re. when they are in the office/lab vs. at home.
And of course there are many advisors (female and male; old and young; with and without kids), who are very sympathetic to the fact that some graduate students and postdocs want to start families during their graduate/postdoctoral years.
So how do you find out in advance which professors have which philosophy? I suppose you could ask potential advisors/PIs directly, but you might harm your chances of being accepted if you started asking about future research disruptions before you even start, so you might want to be cautious about this approach. If this is your #1 issue, though, then you might as well be direct so that everyone knows where everyone stands.
If the direct approach is not for you, you might be able to figure out a professor's track record with previous advisees, or at least try to figure out what a professor's general advising philosophy is. That's important information to know anyway, whether or not you are anticipating a "family event" during your graduate or postdoctoral program. Ask around, chat with current and former advisees, look at personal webpages etc.
Or perhaps readers have other general suggestions or personal anecdotes of the constructive, illustrative sort. Have any of you used direct or indirect methods to investigate the family-friendliness of a potential advisor/mentor?
5 weeks ago