What's sexist about the "that's what she said" jokes? Maybe it's because these jokes never caught on where I live (UK), but I don't understand why would anyone be offended by that.
Any clues? I'd ask my American coworker but she's not in the office.
I think it's an objection to making the topic of sex more prominent at work, rather than anything specifically negative about women. The original bot might have been funny for about one day, and I can imagine getting annoyed at the preachiness of the countermeasure.
As mentioned in other recent discussions here, one component of workplace sexism is treating women as instantiations of a stereotype present only to fulfill male desires. Rather than, say, as competent professionals.
The classic example is having the woman get coffee. Others recently discussed include having the woman take notes or organize a potluck. Related is calling attention to a woman's body in a way that treats her as a sex object.
The "that's what she said" joke could be seen as an example of that women-are-for-sexy-times error. Note that in The Office (the American version at least), the person who makes that joke is Michael, the clueless and offensive boss. That's not an accident.
Any clues? I'd ask my American coworker but she's not in the office.