There is now a second apology, from the CTO this time. It is far better than the first (in particular, it personally apologizes to Monica Cellio), but still misses the heart of the matter. It rightly concedes that nothing resembling process was followed in the de-modding of Monica Cellio, and vaguely promises to create "a process for handling moderator removals, and a process for reinstating moderators who wish to be reinstated". It completely lacks any discussion about the merit of the CoC changes, any opportunity for democratic feedback of the new CoC (only the moderators are being consulted, and the extent to which they are being listened to is not specified), and any acknowledgment of the fact that the rules being pushed are at odds with long-term practice in some of the best-functioning SE communities. Apparently, SO does not trust its own workplace.stackexchange community, of all places, to have an opinion on its new CoC?
As to "actions we can take as a community": I think it is worth delaying any action until Oct 11, when the new CoC is released. There is a good chance that no action will be needed afterwards as all the bones of contention will have been removed from it by then. There is another good chance, unfortunately, that whoever set the Cellio firing into motion will lash out at other moderators in the following days, and there will be enough of a rift in the community that the best course of action will be to take the public dumps, fire up the old MathOverflow software and leave. Everything in-between is possible as well, and a lot of strategizing done now will be hopelessly out of date in a week. One thing is clear for now -- transparency is not to be expected from SO.
EDIT: The new CoC is out. The relevant part is this:
We don’t tolerate any language likely to offend or alienate people based on race, gender, sexual orientation, or religion — and those are just a few examples. Use stated pronouns (when known). When in doubt, don't use language that might offend or alienate.
The relevant part of it appears to be all in the little sentence "Use stated pronouns (when known)", which is a rather harmless-looking request but whose actual reach depends a lot on how it will actually be enforced. (That said, the implicit claim that failure to use stated pronouns is "bigotry" is ridiculous, but I'm letting this slide as a misleading headline.) The FAQ, however, is more disruptive:
We are asking everyone to use all stated pronouns as you would naturally write. Explicitly avoiding using someone’s pronouns because you are uncomfortable is a way of refusing to recognize their identity and is a violation of the Code of Conduct.
For now, we don't know how it will be enforced, but I think we need to keep a site move (via public dumps or likewise) in mind as an option if SE moderators start interfering significantly with the m.se community. (A unilateral site move would, of course, make all existing votes non-attributable, but the m.se community is not overly fixated on counting votes.)