I would assume that there isn't a 'Google Brain Men and Allies' affinity group. "Google Brain" does likely have its own general distro where standard work-related topics are discussed.

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.

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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.