So, here I will briefly (a full analysis would take too long) assess the evidence for or against Danica Roem being a woman, under the concept "woman" traditionally used in English. I will begin with an assessment as I seem to intuitively grasp the concept "woman", since my understanding of the concept does not seem to have changed so it's likely to reflect the traditional one, but also invite interested readers to make their own assessments.
First, when we regularly assess whether something falls into some category (e.g., whether something is a car, a horse, or a chessboard), we don't normally need to have a definition of the concept that picks that category in terms of other concepts. So, I'm not going to try to define "woman", or "man" for that matter.
Still, I will use a number of arguments to at least to narrow down the concept, enough to make an assessment.
Second, some concepts are present in all human societies we know of, e.g., the concept of water, or a morally good person, or being ill or healthy. Other concepts are not like that, and are only found in some societies. Examples are the concepts of a horse, a planet, a train or a senator. Now, some of the concepts in the latter category pick human-made stuff, and others do not. But regardless of which category a concept belongs to, we can generally make proper assessments as to whether it applies to some object. So, the issue of whether gender is a "social construct" is beside the point here, at least as long "social construct" picks things like chess, as a common example.
Third, it's not the case that the term "woman" picks the property of having the inner feeling and/or belief of being a woman. That would be viciously circular. This does not rule out that all women actually have that property and no non-woman actually has it, but at least, the term woman has to be picking something else.
That aside, I will begin with some considerations about how we come to think that a person is a woman, and what we can reckon about the concept from that. This is not as an attempt to provide a full analysis of the concept or a definition in terms of other concepts (which, as I said, we don't normally need), but at least to narrow it down enough to make an assessment.
So, usually, it's enough to look at a person's face to when we assess whether that person is a woman. But that's not decisive. In case the face looks like a woman, but the person has a penis (and other male sexual and reproductive organs), normally we would say that that's a man. However, it might be that there is something that weighs more than sexual and reproductive organs. In fiction, we have cases in which people swap bodies. Let's say that Alice has XX chromosomes, female sexual and reproductive organs, and a female mind. Bob has male counterparts. They swap bodies. Is Alice still a woman?
I think so. While I don't think swapping bodies is possible in the real world (because there are no souls, spirits, etc.), the assessment suggests that our concept is such that, at least in case of conflict, minds prevail.
Now, suppose it's a brain transplant. Would Alice's brain in Bob's rest of the body be still a woman?
I think so, and that gave me reasons to believe minds weighed more. However, after asking other people, now I'm not sure how common those intuitions are.
A scenario in which there seems to be considerable disagreement is one in which a baby is born with female(male) sexual and reproductive organs, but a male(female) brain/mind. If the person grows into adulthood and still has a male(female) brain/mind but female(male) sexual and reproductive organs, would that person be a man, a woman, or neither?
Also, there is the question of how big and permanent the differences between female and male brains are. If they're so small that hormone treatments can change them all or most, then probably non-mental traits prevail. A female body builder who takes steroids is not a man. But then again, it may well be that some of the differences in the structures of female and male brains develop slowly over time (during fetal development, adolescence, etc.), and aren't easily changeable.
In any case, I'm uncertain on this, but I will in the rest of this post hold that probably (but not certainly), a person with a female mind and male sexual organs is a woman. But before I go on, I will mention two other possibilities:
If a person with male sexual and reproductive organs but a female mind is a man, then Danica Roem is a man regardless of whether he has a female or a male mind.
If a person with male sexual and reproductive organs but a female mind is neither a man nor a woman, then Danica Roem is either a man or neither a man nor a woman.
This is a particular problem for leftists, because it's a usual leftist belief that there is no such thing as a female mind or a male mind. But if that is so, then a person with male sexual and reproductive organs is a man, and that's that. Since it's clear to me that there is such thing as a male and a female mind, I will go on and assess: Does Danica Roem have a female mind?
Roem normally developed male sexual and reproductive organs, as well as male secondary characteristics, from Adam's apple (much larger in males than in females) to the structure of the shoulders, etc. Nearly always, a person with those traits has a male mind, so that's very strong evidence that Roem has a male mind. It seems that in order for Roem to have a female mind, a lot of things would have to have malfunctioned.
What's the counterevidence?
Roem claims to be a woman, and that's some evidence, as Roem has more information about Roem to make the assessment. But Roem does not have better information about others, and in order to make the assessment that Roem is a woman, Roem needs to compare people in the two categories (men and women) with Roem, and conclude on that basis that Roem resembles women more than Roem resembles men.
But a malfunctioning in the part of Roem's brain/mind that makes that comparison and makes the categorization seems more likely to me than the sort of malfunction(s) that would have led to the full or even predominant development of a female brain.
Now, there are some studies that show that the brains/minds of people with male sexual organs but claim to be women are in some ways female-like to an extent. But the evidence I've seen at most points to a mixed of male and female characteristics, not to predominantly female minds. If so, given the rest of the properties (e.g., male sexual and reproductive organs and secondary traits), it semes probable that Roem is a man to me - or if not, at least not a woman.
But can the inner sense of whether one is a woman be mistaken?
Sure, since (among other reasons):
a. It seems that that inner sense can only operate by means of assessing whether one is more similar to women than to me, or the other way around. So, in addition to information about oneself, it needs information about others, and then compare them. There is plenty of things that can go wrong, regardless whether that inner sense results from a dedicated system of the mind or is the result of more general mental processes.
b. We know it failed in the cases of those people who change their mind. For example, there are people with female(male) sexual and reproductive organs who claimed to be men(women), and now claim they were mistaken. There are examples that don't involve Christian beliefs, or Muslim beliefs, etc. They may be a minority of people making transgender claims, but it shows that the system sometimes fails.
But perhaps, there are more studies about transgender people I haven't read, and such that if I were to read them (eventually, I will probably read more), I would change my mind on whether Roem probably has a female mind. If so, then I would have to go back to the issue of what prevails in case of conflict (i.e., minds/brains vs. sexual and reproductive organs). If you have evidence you think is decisive or at least good enough to make it probable that Roem is a woman, links are appreciated.
Before I address the issue of whether the meaning of the words has changed, I have a few attacks to reply to, so I'll get to that.