On Individual Characters vs. Broad Trends
This, I believe, is a flawed judgment, for the reason that some individual women are, in fact, prone to overemotional reactions.
This is not because they are women.
This is because they are human, with any of an assortment of personality quirks that come along with that condition. I know more than a few men who are prone to such an overreaction.
And perhaps, one might say, it would have been better to use a male character for that role - to make a man overreact instead of a woman, to deter the accusations of sexism.
I disagree. Women are approximately fifty percent of the human population, and it is probable that approximately fifty percent of overemotional freakouts are had by women. Simply because years of consistent portrayals of a trait as a quality exclusive to women has made it a sensitive subject does not mean that this trait can never again be ascribed to women in fiction, nor does the ascribing of such a trait to one character mean that the writer is sexist. For that to happen ,the writer has to consistently portray the majority of their female characters as overemotional basket-cases - have a look at a good many sitcom writers if you need an example. Having one character with this trait is not sexism, it's having a character with believable human qualities - or, in the case of some works of amateur comedy, somewhat unbelievable human qualities. Even exaggerating these traits to absurdity in one case, however, does not make the writer a sexist - anymore than making a male character an unbelievably smug windbag suggests a belief that all men are cartoonishly smug windbags.
When writing fiction, it isn't healthy to constantly be looking over your shoulder to make sure that nothing you write could possibly offend someone. Just write natural characters that fit the story you're writing. And even if you can't do that, a bad joke doesn't make you a bigot - perhaps a bit thoughtless, and certainly not a master comedian, but not necessarily a bigot.