This is flatly contradicted by both Caleb's post (upon which this whole thread is based) and Monica's.
Caleb resigned because the new rules proposed would not allow him to compromise by simply referring to trans people by name and avoiding all pronouns. His issue is not that he insists on using "he" for a transwoman, but that he refuses to use "she", and would rather stick to names.
Likewise, per the from-memory transcript she posted, Monica - who has no issue referring to a person who has changed gender by their preferred gendered pronoun! - simply stated that she often prefers to avoid the singular genderless "they" when referring to a specific person, and so would prefer to refer to a person who has that as their preferred pronoun by name. That, apparently, was enough to get her fired.