This is a commendably thoughtful article, but you've omitted another possibility: realist necessity but nominalist sufficiency.

That is, gender dysphoria is necessary (or some other statement akin to "strong and irreconcilable mismatch between physical sex and mental self-perception of what sex should be"--it needn't necessarily be dysphoria). But it's not sufficient, and the additional criteria are decided not with conjunctions and disjunctions but rather organically by examples, a preponderance of other qualities, and so on.

I think you also too glibly dismiss the philosophical implications of the medical angle of transmedicalists. It is broadly accepted that we have differing obligations as members of a morally upright society when it comes to alleviating suffering when something is actively "wrong", and it enabling people to achieve their goals. Indeed, you can see people who are absolutely not truscum very quickly resort to the former type of arguments when challenged, despite not having the philosophical foundation to fully support this type of argument.

Concretely, consider the distinction between reconstructive surgery to fix cleft lip, and cosmetic surgery to give oneself fuller lips. It is generally not considered controversial that cleft lip is a serious medical condition and that we should go to great lengths to ensure that children born with cleft lip have surgery that will fix the defect at least enough so they avoid the worst of the consequences. Furthermore, even if the person ends up conventionally not very attractive, we understand that it's making the best of a bad situation and are highly sensitive about making harsh judgments and instead try to support them to the extent possible. A medical problem demands a societal response. However, it is equally uncontroversial that while a liberal society should allow people to get lip augmentation, it is not the responsibility of the rest of us to pay for their beauty goals--and if we don't like the result, while we still could be expected to ideally be cordial about it, that is as far as it goes.

It is precisely the medicalization of gender dysphoria that provides the strongest argument that the societal response should be supportive in the way that we are supportive to people who suffer from cleft lip.

Furthermore, there is substantial evidence that this is not merely an abstract point of debate but reflects widespread attitudes. (Attitudes can be changed, but it is important to understand where one is starting from.) YouGov's poll of attitudes towards transgender people and issues in the U.K. indicated a striking split between acceptance of trans women who had undergone gender reassignment surgery in situations typically limited to women, and between acceptance of those who had not.

Though you argue pragmatically that people who need such-and-so gender affirming care should get it either way, you have done nothing to justify the "need" under a nominalist account aside from putting the word in italics. If we continue to not consider hair loss treatment a "need" (for balding men) and breast augmentation a "need" (for cis women) and so on, a nominalist conception of trans identity threatens society-supported care by threatening the notion that need can be distinguished from want. Society is not entirely consistent on this point inasmuch as orthodontics to straighten teeth is typically covered by insurance, despite being almost entirely not a "need". But one can legitimately be concerned that gender-affirming care would not necessarily get the same exception.

I would note that the realist/nominalist distinction is actually not so clear cut as you use it. If you deconstruct your terms into more sub-terms and then create a synthetic term from those sub-terms that lies along the axis normal to a separating hyperplane between two clusters (basically, linguistically create a support vector machine classifier), you can in principle create a single axis along which variation falls, and pick some appropriate point (e.g. a local minimum) at which to cut, and thereby turn a nominalist mixture of different qualities into a single axis with a clear (or at least clearly stated) demarcation point as a realist would like. If you can do this, the realist can say that there is a real difference there (inasmuch as you can ever say there's a real difference when you find two clusters). The only problem was that we hadn't previously bothered to make it easy to talk about that real difference because we hadn't the right words to do so. In practice, this is onerous and so I agree that reflective equilibrium is a better approach in practice (but this does not entail that the distinctions are not real, just that we might change our minds about how to classify borderline cases).

Finally, although you do not touch on this, the realist account, if sufficiently supportable by evidence, has strong implications for a society in which gender-based gatekeeping is commonplace. That this is important is exemplified by the strife over the idea that "trans women are women". A realist account, in principle anyway, could make the case that yes, objectively, in very important ways, trans women are women. A nominalist account has trouble doing more than making the case that as a matter of cultural convention we insist that when you utilize the word "woman" to mean "trans woman or cis woman". And, of course, if a group of people are insisting, without clear correspondence to reality, on changing language, other people are free to simply say, "No."

Put simply, if (the right flavor of) the realist account is correct, gender gatekeeping ought almost automatically accept trans people of the gender they identify as. If one cannot formulate a credible realist account, gatekeeping remains unresolved and is a separate negotiation to be had between various stakeholders in society.