It doesn't seem like a hate group to me. The idea of masculinity IS toxic, virility is not an ideal that should be imposed on anyone. This seems less like a "hate men" and more like "hate masculinity being an ideal men are supposed to adhere to"
And it's not even that Harvey Mudd is the exception from that list. Pomona, Pitzer, Vandy, Duke, Dartmouth are all ridiculously good. You would actually have to be insane to disregard those because of the existence of a club you disagree with.
If she can't write possibly the simplest program there is, she shouldn't be in the same class as people who have actually spent time learning how to code. It has absolutely nothing to do with her being a woman.