Even if there are cases in which it would theoretically be reasonable to employ different priors for men vs. women, I doubt people will be able to reliably identify these cases, choose appropriate priors, and correctly apply the priors they’ve chosen. When you couple these challenges with the fact that there are significant downsides associated with trying to discriminate in a principled way (e.g., harming people, alienating people, creating self-fulfilling prophesies, making it harder for members of an already disadvantaged group to succeed, etc), it seems like a bad idea to base priors on the variability hypothesis in basically any context.
Even if there are cases in which it would theoretically be reasonable to employ different priors for men vs. women, I doubt people will be able to reliably identify these cases, choose appropriate priors, and correctly apply the priors they’ve chosen. When you couple these challenges with the fact that there are significant downsides associated with trying to discriminate in a principled way (e.g., harming people, alienating people, creating self-fulfilling prophesies, making it harder for members of an already disadvantaged group to succeed, etc), it seems like a bad idea to base priors on the variability hypothesis in basically any context.