If you're not white, things are different.
Can you think of some examples of when you were unexpectedly forbidden from participating in an event/group/etc? Did you have access to alternatives?
2. There are lots of people who lived through the Civil Rights movement alive today, and segregation and the associated attitudes didn't disappear overnight. Do you think 70 year old politicians carry no baggage from their upbringing and early adulthood?
I suspect men-only clubs for traditionally female dominated fields, something like an all male kindergarten teacher group, would be broadly accepted as reasonable.
Nursing, home healthcare, child care, veterinary services, social services, and libraries are the other canonical examples besides education of highly women-dominated fields where having male-only employee resource groups might make logical sense.
I'm not sure I agree with you that it would be broadly accepted as reasonable, however, even though I personally would find it reasonable.