Thanks for the interesting comment.

It feels like what you're describing here is what I'd use the words masculinity and femininity for. You do indeed use that term in the third paragraph. If someone said "Please define a form where someone can specify their masculinity or femininity" then I'd consider the request rather odd, but I'd also immediately imagine a slider. As indeed, I'm sure everyone has met people who whilst possessing the anatomy of a particular gender behaved more like the opposite, in terms of behavioural stereotypes.

As there are already words to describe this spectrum and the existence of it is uncontroversial, I struggle to understand why there's an academic attempt to redefine the word gender. It feels abusive, like the behaviour described in 1984 or Animal Farm, where people play games with language in order to create artificial crimes they can accuse their opponents of. If all these people mean by "gender is a social construct" is "there are masculine women and feminine men" then why don't they just say that?

Over the years I've come to learn that people who are paid for their production of ideas are often tempted to obfuscate their language in various ways, or at the very least, aren't bothered by their field redefining standard words in ways that have unintuitive meanings. This behaviour isn't organised or deliberately malicious, it just arises from the incentives they have to carve out an intellectual space in which they make the rules and other people find it hard to enter. It's difficult not to conclude this is happening with the redefinition of the word "gender".

If you don't know much about math, you probably aren't going to tell people with PhDs in math that they are wrong because you don't understand what they are talking about

Actually I have told people with PhDs in maths things to that effect ;)

Cryptography is essentially (semi)applied maths. Mathematicians and theoretical cryptographers do have an unfortunate tendency to redefine standard mathematical terms and operators to mean something different in different contexts, or sometimes even things that are misleading. For example they like to say, "we have proven this scheme correct in the generic group model", which means a proof has been provided that assumes attackers can only solve a very small set of allowed equations and thus doesn't prove much of anything. Yet to anyone outside the field it sounds very impressive, like if there is no flaw in the proof then the proposition is completely true. They also like to redefine the meaning of + and * in some contexts, like when working with elliptic curves, such that equations that look like normal math actually mean something totally different. They could use different symbols or even words, but, they don't.

There's often no need for this. Jargon is unavoidable in any technical field but often phrasing things in plain English loses no precision and can only illuminate. Gender/critical theory seems to be filled with bizarre redefinitions of terms to mean the opposite of what they normally mean, like the way they pretend racism means something else such that their obviously racist statements, by their definition, aren't, and statements that aren't racist by their definition are.

I've found over time that I prefer reading papers from corporate research teams, as they tend to engage less in this sort of obfuscation.