Have you ever attended a mandatory DEI meeting? The entire premise of that industry is to tell you which slurs are acceptable (ie: cisgender ) and which are not.

Very few of the people saying "cisgender" say it in a way that suggests sixty years earlier they'd have dragged me behind a car for having the temerity to be that way.

"Cisgender" is a slur the same way "male", "heterosexual", and "white" are (I am all three; four, including cisgender). In other words, it is not a slur.

Slur isn't an intrinsic property of a word: it's a property of how it's used. "Male" can be a slur, as can "heterosexual", or "management". In theory, "cisgender" can also be a slur, though I've never heard such a use. (You'll sometimes hear "cissy", but I've never heard that used against a specific person.)

You might argue that "punching up" is acceptable, or even that it's not slurring by definition (which I'd dispute), but membership of one "privileged class" doesn't automatically translate to actual privilege. (I think the feminists call this intersectionality.) In such a context, the labels of "privileged classes" absolutely can be used to punch down (e.g. saying "you're such a man" and slamming the door in the face of an impoverished gay transgender man trying to access domestic abuse services).

The usage of the word "slur" in question -- it has to be this if it's on a list one can learn from DEI consultants -- is

    a derogatory or insulting term applied to a particular group of people.

It is inherent in the term itself, not in its use.* So it isn't simply anything that can be understood as an insult. All the stuff about "punching up" and so forth is beside the point.

"cisgender" has a technical meaning which is still it's primary use: someone who identifies with the gender they were assigned at birth (so it can apply to intersex people as well). In this it is like "heterosexual" and "male". Arguably it is not like "white", in that who counts as white is malleable, but for the most part whatever it is, in most contexts, "white" is not a slur either.

* I am in fact a lapsed linguist. I have a PhD. My specialization was in semantics and pragmatics. Semantics is meaning encoded in language. Pragmatics is meaning inferred from use: "it's cold in here" meaning "shut the window", for example. I am aware that one can talk more precisely and at much, much greater length about all of this. But this is Hacker News, so this is all I am going to say.

By your given definition of "slur", neither "management" nor "cissy" are slurs (except in the sense of "cissy" as a variant spelling of the slur "sissy").

I'd say "white" is no more or less malleable than the others. "Male" has multiple, mostly-overlapping definitions; by extension, "heterosexual" and "cisgender" are likewise flexible, though "heterosexual" has additional flexibility. While the concept of "white" is completely ungrounded in base reality, as a cultural term (a description of how racists categorise people, and of who's affected by the consequences) it's relatively stable: the definition in Western Europe is completely different to the definition in North America, and the boundaries have shifted over the centuries, but contemporary racists in a given racism-domain seem to agree with each other.