Well, isn't this the whole problem right here?

Since when did rarity give a license to beat someone bloody?

I think you're choosing an unhelpful, possibly even pernicious definition for the word "construct". Typically, the word is used for something that we build, not something which already exists without our judgment or labor. To say "gender is a construct" is fair, because we have decided to use the word "gender" specifically to refer to the social constructions. But to say "binary sex is a construct" is liable to be gravely misleading, as it is not like "race is a construct" (like, why are people whose ancestral origins are 75% from Europe and 25% from Kenya considered the same race as 100% from Namibia?!--parts of what we call "race" are biological nonsense) or any of the other things where we highlight the arbitrariness of the distinction.

I would not say that evolution, or evolutionary pressure, or any such thing is a "construct". That is simply the wrong word to use. The theory of evolution explains a natural process, and there is absolutely regularity in the kinds of random mutations that are selected because not all things are equally adaptive (hence convergent evolution).

You seem to be suggesting that we should, because people are too stupid, lie to and/or trick them for their own good and for the good of society. ("entirely reasonable... But in a social context...often without the insight") To the extent that this is your position, I stand vehemently in opposition. You cannot reliably reason from lies, as they are uncorrelated to reality, and you cannot robustly keep people believing lies because the evidence is there and when they learn they're liable to disbelieve everything you have told them (strictly speaking, a fallacy on their part).

So, if the problem is that people don't understand biology well enough to know that cats and rabbits can't interbreed then let's teach them some biology! They're not stupid, just poorly informed. If they don't know that XXY individuals are about 0.1% of children, well, let's teach them. We can teach about gender dysphoria, about sex-specific neural development, whatever we need to.

But fundamentally, most people do (contrary to your characterization) recognize our fundamentally common humanity. If they are not excused from compassion by some ideology or threat to their group, people can be quite lovely to those who they know and connect with on a personal level, even if that individual has some rare phenotype.

So I reject that there is any wisdom in distorting our view of biology to serve what we conceive of as a noble social goal. Connection, not dishonesty, is the route to a more tolerant enlightened society.

You ask in your hypothetical what good I would have done to be accurate? I would have stood with reality. That is enough.