First things first: we do need some solution to the problem that she faced, and it is a real problem, that relates to gender. That said.
> How much will it take to convince the average HN reader
that sexism actually is everywhere?
In a sense, it obviously is. But I want to reflect a bit on what that might entail.
You will note (see https://news.ycombinator.com/item?id=16390786) that the amount of sexist threads was 14 per week, which, in the period of 3 months with 2100 messages, gives about 1% of messages.
For reference, the DSM gives the prevalence of psychopathy at 3% for males and 1% for females (https://www.quora.com/What-percentage-of-people-are-psychopa...).
So, even though this sexism is a societal problem (in the sense that it exists in our society and is hard to extricate from comunities) it is not clear that sexism (or at least the sexism displayed in the article) is a problem with a social solution: teaching children (or people in general, as it may be) that this is not OK probably would not reduce the problem much further.
I predict, therefore, that no amount of society-wide measures against sexism can reduce this (very marginal!) behaviour (if the chat itself remains consequence-free for the users). That is: that fighting sexism is not gonna help this at all, and we'd need other, technical and local-to-the-website solutions.
> How much will it take to convince the average HN reader that sexism actually is everywhere?
That it is everywhere, in the sense that some (few) people bring it everywhere, not much. That it is everywhere, in the sense that all of society is guilty of it and each person should try to fix it in themselves, evidence of an entirely different sort.