The problem here lies in the word "sexism" and that, I think, you believe a solution should be to remove its baggage. The replies you get are, I think, because many people, with good reason, believe that such a goal isn't feasible. In fact, the baggage itself is probably why you perceive the replies to be "emotional".
So I go back to my first reply: to stop casting people into a binary like I think we both want, better not to throw such loaded words at people and instead analyze their behavior on a case by case basis. Fighting the word itself is prescriptive at best, and language tends to be descriptive, AFAIK.
I'll push back a little, but it seems we're pretty much at consensus. We have to recognize that people use words in vastly different ways, especially as we're enabling more cultures to communicate. Around me "sexism" has this broader meaning and subsequently doesn't necessarily hold as much weight as the binary usage holds (though it can, but again, continuum). Unfortunately language is extremely imprecise and the dictionary not only lags societal definitions, but only reflects certain usages. Because of this it is important to recognize that language has multiple parts. There's: What someone says, what they mean to say (the information they are trying to convey through a function with limited expressiveness, i.e. language), and what is heard. If we don't recognize that these three things can result in three different interpretations then we're going to continue to have many of these problems. Rather if we look at language as the imprecise means of transporting information from one person to another it means we should rely less on the actual words said and more the intended meaning. This is more difficult to do, but it is something we commonly do with friends and people we know well. We need to apply this same restraint to others we don't know as well.
So if we're communicating with words meaning different things (which is extremely common but unnoticed) then we have to be careful that we don't lose meaning on the assumption that someone's message can only have one interpretation. We have to recognize the embedding problems and limitations of language to effectively communicate.
So I go back to my first reply: to stop casting people into a binary like I think we both want, better not to throw such loaded words at people and instead analyze their behavior on a case by case basis. Fighting the word itself is prescriptive at best, and language tends to be descriptive, AFAIK.