I don't work at Google; I work at Amazon. I can only speak about my experience, but it's likely the same at Google.
You don't have to be a part of an affinity group to be a member of the mailing list (that's where the ..and Allies portion comes into play).
The 'Google Brain Women and Allies' mailing list is probably full of women from the Google Brain team, non-binary and men from in from the Google Brain team, and others who aren't on the Google Brain team but are interested in its work.
Again, I don't know. But this is educated conjecture based on my experience at another FAANG.
At the hazard of becoming 'political' and triggering people, affinity groups are typically created for groups that have traditionally been underserved, marginalized, or have special considerations.
As a cis male, I don't really see the need for a 'Google Brain Men and Allies' distro list because the issues that men face in the workplace are generally the same issues everyone faces. Women (and nonbinary people) can be confronted with issues that men simply aren't.
---
At Amazon, there are groups for Black employees, Latinx employees, LGBTQA+ employees, transgender employees, women, disabled employees, etc.
Sometimes these groups talk about work; but sometimes they talk about just life things. For example, often cisgendered employees will have children that come out as trans. So they'll reach out to the transgender community for help and support as to how to be the best advocate for their child.
Or, as a personal example, I moved to a new city to take the job at Amazon. I was looking for a therapist, and it was important that the therapist be supportive of LGBTQA+ issues and ethical non-monogamy. So I reached out to the LGBTQA+ group for therapist recommendations.
But when I hear about a 'Google Brain Women and Allies' distro, I'm more thinking about peers which discuss things which impact them. I wouldn't get too hung up about the 'Google Brain' portion of the distro; it's likely just a way to self-select a group of peers which share a common interest.
Gender equality activism has been part of US politics since at least 1776: http://www.thelizlibrary.org/suffrage/abigail.htm (Abigail Adams advocating to the constitutional convention)
Is there an affinity group for the overwhelming majority of "Latinx" people who don't use or like this term?
In my opinion, this leads to division and contempt/hatred for the other group. I live in a super progressive US state, and the university near me got a lot of backlash for hosting White affinity groups.