I disagree with you that there is no reason to do so for “non-sexists”. Because no one knows how a given person may interpret a given conversation or activity, combined with the severe consequences from the social media mob that even something as simple as an unsubstantiated tweet can inflict on one’s career or an entire company these days, the only way to avoid liability is to minimize interaction between opposite sexes in the workplace. In this environment, it’s the only rational thing to do.
We have unleashed a virtual lynch mob, ready to instantly torch the life of anyone that stands accused of even moderately inappropriate or questionable behavior. Worse, there is no statute of limitations or standard of proof required to activate the mob - a tweet is enough. That is wrong and creates a toxic environment for everyone.
In other words, people who "battle sexism and discrimination" can very well tip over and become sexist and discriminatory in the attempt to fix those exact issues.
They can become Monsters too.
The second part of this quote applies to. "If you stare long enough into the abyss, the abyss gazes into you".
If you fight sexism and discrimination long enough, you yourself will go under the spotlight and you'll eventually be judged for what you did. Whether good or evil.
If a man accuses me of sexual harassment, that would be pretty easy to disprove (I’m straight) and most people would believe me. If a woman accuses me of that, in a MeToo world, my career is over, even if there is no evidence and I didn’t do it (being that we are living in the MeToo world, I guess I should say that for the record I have not ever knowingly sexually harassed anyone, and have never been accused of it).