It's a bit confusing because a mod was removed, and a bunch of other mods resigned in support, and then it came out that she'd been removed for refusing to use people's preferred pronouns.

Stack Exchange is perceived by many people to be unwelcoming. There has been persistent concern that SE is even more unwelcoming to people with protected characteristics.

SE have made considerable effort to fix this.

Recently they've been looking at codes of conduct.

The most recent version of this includes a request, or maybe a requirement, to use a person's preferred pronouns.

Some people refuse to do this because God tells them it's wrong to do so. Other people refuse to do this because, well, I dunno I've never understood why calling someone "he" instead of "she" is such a burden.

Stack Exchange is telling those people that their refusal to use a preferred pronoun is not compatible with being a moderator at SE, and so they removed one mod.

She posted her version of events to one of the SE sites, and this caused a bunch of other mods to "resign" their posts in support of her.

EDIT: I've tried to word this as neutrally as I can.

To respond to a couple of comments: Bob says "please use 'he' when talking about me, and Ann says "No, I can't do that because God tells me it's wrong. I'll use 'them' instead." -- I don't see how this can be anything other than Ann refusing to use Bob's choice of pronouns. Note that I haven't used the word "misgendering".