How to react to an angry email / argument as a third party
I would suggest that the proper etiquette here is similar as to how you should behave if you were to witness two people arguing in public. You may listen—the argument is, after all, public—but you probably shouldn't interject unless you are directly addressed. As stated in the comments, this is a very common tactic for raising the stakes in any discussion. This currently isn't your fight... don't get involved unless you want it to become your fight (pro tip: you don't).