> People-first language (“enslaved people” not “slaves”)
“enslaved people” is not people/person-first language.
“People who are enslaved” is people-first language.
“enslaved people” is “situation first” (more commonly “identity first” or “disability first”, but neither strictly applies to “being enslaved”) language, just as “slaves” is. (In the disability context, “the disabled” and “disabled people” are textbook examples of “disability first” language, to which “people first” or “person first” language is contrasted.)
EDIT: Yes, I realize that this is an example of "people-first" language given near the opening of this opinion piece. It says something that in this rant about "equity language", the example given of the application of a particular form ("people-first language") of equity language is basically a textbook example of what that form seeks to avoid rather than what it prescribes.
> For example, it seems like we can’t say “mother” anymore in medical settings.
You can absolutely use “mother” to describe a specific person who, in fact, is a mother in medical settings. Because people of non-feminine gender identity can give birth, it is sub-optimal and exclusionary as a generic term for a person giving, or who has given, birth.
> I support trans people living however they want, but my mother was a mother
Literally no one has a problem with your mother being described as a mother.
> At work, a “women in engineering” group got renamed to something bland like “gender minorities in tech”.
Presumably, it got renamed that because whoever made decisions for it decided the mission was broader than women. “Gender minorities” isn’t a bland alternative to “women”, it has a broader scope.