Don't agree with the comments above and generally support DEI initiatives, but I also have an example.
A new DEI director joined a previous employer and started a mandatory survey to affirmatively label everyone's trans status. Whatever you entered would be used to auto-update your public info page with details on whether you identified as trans or not, with no opt out. I hope I don't have to explain why that's ill-considered at best.
Anyway, refusing to fill it out immediately escalated to a disciplinary meeting with the director.
This isn't a good example, because this isn't "walking on eggshells", this is an example of a misguided policy that has unintended consequences, and in your own example, when they understood the unintended consequences, they removed this.
Sure, this person was probably bad at their job, and that's problematic, but this isn't an example of someone being fired because they said something non-problematic.
Correct, they didn't remove the policy or change their views on the surrounding context of the disciplinary meeting. They simply understood the issue after it was explained to them. It's not a high bar.
The director was a trans woman themselves, just not good at their job. At least they recognized the issue when was pointed out to them in that meeting, but this was just the tip of the iceberg for silly changes they pushed.
A new DEI director joined a previous employer and started a mandatory survey to affirmatively label everyone's trans status. Whatever you entered would be used to auto-update your public info page with details on whether you identified as trans or not, with no opt out. I hope I don't have to explain why that's ill-considered at best.
Anyway, refusing to fill it out immediately escalated to a disciplinary meeting with the director.