In particular, the controversy surrounding Damore's "manifesto" seems very hard to understand if most people believe that there are differences between the genders that could affect the "outcome"/gender gap in tech/whatever. If this in fact what everyone thinks, then why are so many people upset that someone wrote a document saying this is the case? The whole thing should to be a no-issue? (I guess some of the points of Aaronson's original blog post might be applicable here. But I'm not sure that really improves the situation...)
Secondly, if everyone agrees that there are differences between the genders that could affect for example the gender gap in tech, I have a very hard time understanding how one can routinely blame more or less any difference between the genders on discrimination or some such.
You're changing your original summary of the argument by adding the qualification "that could affect the outcome". The whole question at issue is whether the differences that there are between men and women would be expected to have a significant effect on outcomes in tech.
https://www.youtube.com/watch?v=kasiov0ytEc
Not a really exotic belief in the core social justice circles.
Though advocates tend to avoid stating it outright, since it's so easy to attack and so ridiculous. So it's generally left implicit. E.g. They'll just say, "X field is only 30% women, we must fight the sexism that causes this", leaving it as an unstated assumption.
Really? Could you give a reference to anyone ever actually making this argument?