Might be that my interpretation of history is too literal since I think the reasons feminism existed in the first place had more to do with stuff like voting rights, freedom to work and equal pay, freedom to make sexual and health decisions, an end to religious oppression aimed at women and similarly important issues rather than insinuations and (arguably) distasteful jokes on the internet.
As for people judging her on her looks on the internet, yeah, that would never happen with men...
(I would include a picture of Sam Allardyce too, but I wouldn't want to lose my lunch or have google record me doing a Sam Allardyce image search - there are some lines I don't want to cross on the internet)
As for the assumption that this was a feminist in the first place, the point is that this is funny because it could be. Some modern self proclaimed feminists have gone far enough that they are quickly closing in on Poe's law territory if they're not well within it already. In other words they're getting to the point where it's becoming almost impossible to separate them from people parodying them. Seriously, I wouldn't have been surprised if this woman came forward and said it was just a cube she was carrying to work or if she came forward and said it was a personal space box. That's part of what makes it funny.
If there's a male activist group or label that is beyond parody in a similar fashion I don't know about it, but plenty of men are part of other groups that are similarly ridiculed.