"Douchebag" is gendered, I guess. It's not clear to me that it's sexist. In common usage, it virtually always refers to a man. The actual relation to a "douche" is mostly vestigial.
I think you have to let this one go. Fighting against linguistic churn as a proxy for "sexism" seems to me like it hurts more than it helps, as it feeds the "PC feminazi" meme. There are better fights to pick than this one.
Seems like its use as a nickname/insult really exploded in the 70's and 80's. I'd tend to agree that tying the word to sexism is a bit of a stretch--it's probably just being used because it sounds like a naughty word, and anything more explicit or profane wouldn't get past the censors.
I think you have to let this one go. Fighting against linguistic churn as a proxy for "sexism" seems to me like it hurts more than it helps, as it feeds the "PC feminazi" meme. There are better fights to pick than this one.