The issue with "female hysteria" is that it was seen as weak, imaginary, illegitimate, etc. It was never accorded proper research (which treated women as equal participants) and was treated as a sign of inferiority.
That is still the issue with menopause today. You and the poster you quoted are so afraid of the stigma around even admitting that the menopause is an issue – especially in a male-dominated society – that you'd rather just pretend it doesn't exist. It's shameful to talk about this issue, let alone acknowledge it can have the worst consequences (as in NB's case potentially). Anyone who suffers from it is just weak, and letting the female sex down in front of the men!
Period cramps / endometriosis used to have the same status as the menopause: "Throughout history this pain was routinely dismissed as psychosomatic, the result of poor lifestyle management or punishment for delayed pregnancy. It was frequently denied the status of real pain... There was a genuine belief that women who experienced severe pain on ovulation and menstruation were making it up."
Not every woman has period cramps, but many do. Imagine if it was deemed shameful and "sexist" to talk about period cramps, just because it's an ailment suffered only by women. Imagine if society had never said "actually, this is quite a widespread issue and can have devastating consequences for some women". Legitimate research would not have been conducted. It would still be a "sexist insult" to say that someone suffered from period cramps, and the vast sub-section of the population with actual period pain would not have got any help.
The menopause affects a lot of women negatively in terms of mental health – not me personally, but a lot of women I know. As I've said before, female researchers have called for more funding, research, attention and legitimacy for this issue. They have said that if it affected men instead of women, lots of research would already have been done about it. It would be talked about in scientific rather than shameful terms.
So yes, if you don't acknowledge the menopause as a legitimate scientific and biological issue faced by much of one half of the population, then yes, it risks turning into this era's "womanly hysteria" – a poorly understood, mislabelled, stigmatised, hush-hush, erroneous label for actual specific medical issues.