I think this question kind of narrows the situation a bit. Here's the context I would give.
There's been problems with acceptance of the Lavender/LGBTQ+ community for a long time, and it's been swept under the rug for a long time. Not going to share too many specific details, but there have been mod resignations because those mods felt uncomfortable/unsafe due to their status as a member of the community, there have been...less than pleasant comments, both in the Teacher's Lounge and outside of it, etc.
This has been going on for a while, by which I mean for years and years, on the network. It's also worth pointing out that discrimination against the Lavender community is an issue that extends beyond the network, big time. Like - this is a hundreds-of-years, around-the-globe, beyond-the-internet issue. With that comes even more context that I could spend hours giving. (I'd recommend reading up on the broader context of the issue a bit - it'll help with the vocabulary being thrown around a lot here, at minimum. Wikipedia is pretty good at this.)
Then you have the Welcome Wagon, and similar initiatives coming along. It was poorly handled (implicating some of the high-rep users who were doing their level best) and SE caused backlash...which probably caused more of an instinctive "we're right, we've got to handle this our way" approach from upper SE management. You've also got a rise in movements, especially in the U.S., in favor of the LGBTQ+ community (which is a really good thing, but adds to the pressure on SE to do something about this situation they've let fester).
Into this increasingly complicated and tense situation comes the new Code of Conduct update. (I should note that at its core, this is a very positive improvement in my opinion, and I wholeheartedly endorse it. It's the context that makes it all so very messy, as is often the case.) Monica asked some clarifying questions. I'll quote some comments I made recently that I think summarize the issue reasonably well:
Monica refuses to use the pronouns they/them [she uses all other pronouns, including neopronouns, when asked].* This is problematic and painful, especially when it's targeted at a specific group that is often marginalized to begin with. Monica has her own personal reasons** for not using those pronouns [...] Unfortunately, when Monica attempted to share these experiences, the phrasing she used - reasoning about "grammar" and "compelled speech" [I say this all from having read the transcripts extensively] echoed common arguments from people who have much worse motives than Monica did [...] These are classic 'arguments' when talking about these issues, and so they became signal flags. Talking directly with Monica, I don't believe she had the broader intent that most people using those arguments do, but nevertheless what she said hurt. The unfortunate language she used, and her repeated insistence on not using they/them meant that she became an...easy scapegoat to Stack Exchange in the middle of a broader, far more complicated issue that has been festering on the network for years.
In other words, I think what happened here is: SE felt like they'd ignored a broader situation for too long (they weren't wrong there), so they came down hard on the first incident they saw, which is obviously...not the best response, especially since their "coming down hard" apparently involves libel.
I also think what you note about "Possibly this is what happens when people do not communicate face to face and do not even really know one another" is really accurate. SE has unfortunately fallen into a pattern of a minimum of communication and feedback, and this has, I think, lead into a large number of their problems.
The thing is, they now have themselves in a situation. Having committed libel, they have put themselves in a position where legal stuff has probably tied their hands in some respects, and it's now all tangled in red tape.
There's another perspective to this: what some argue is the general toxicity of the Teacher's Lounge. It is well known that more than a few mods have quit the TL because they feel it is a toxic environment in which it is hard to have reasoned discussion. So...that's in there as well; I can't share much beyond that on that aspect.
* While this sounds like not a huge deal, I find it more helpful to reframe the issue this way: I have a friend who is a trans man. If I said to him, "I respect you, but using he/him pronouns bother me fundamentally, so I'm going to reword my sentences to not have any pronouns" - no matter how well and naturally I phrase my sentences, that will be painful for him to have his identity discarded like that because I "was bothered".
** Monica elaborated on this slightly: "My avoidance of singular "they" is not mere convenience/preference or even mere grammar. I tried to explain the deeper identity issues to heather, and also to a CM in email. (Also tried in TL, but people didn't seem to be listening.) But I am not going to post deeply personal stuff like that for the whole Internet; you'll just have to take me at my word that there are real reasons and it's not just fluff. I would never knowingly use the wrong pronouns, and I'm a good-enough writer that my natural, ungendered writing is not conspicuous. I can't do anything about witch-hunts, of course." Monica also, writes in a gender-free manner in general, which is highly commendable. She also elaborates on it in a comment on this question.