Where nominalism fails is in its rejection of any metaphysical or essential aspect of being trans. If transness isn't essential, then it isn't real; and, if you follow this line of reasoning to its necessary conclusion, there is nothing left but despair. Meaning is an inherently transcendent quality, and rejection of transcendence is rejection of meaning itself.
It is one thing to speak of who is trans, and another to speak of who is regarded as trans; and failure to recognize this distinction leads to a mare's nest of difficulties. In the end, "gender" and "transgender" are words based in subjective experiences, from which -- unless we are nominalists -- we infer objective reality. Reality necessarily incorporates boundedness, a distinction between this and that; if gender is real and there is more than one, then there is a real boundary between what a gender is and what it is not. Nominalism would erase this distinction and substitute a purely relativistic understanding of gender; and I think this is because nominalists are deeply suspicious of boundaries, of limits. If a boundary exists between this gender and that, then it is theoretically possible to bless one claim of gender diversity and not bless another -- and distrust of this power, because it can be misused, leads them to reject the idea that gender is objectively real. But fear is not science.
"The deep metaphysical worry for truscums is that if we don’t have a clear bound of what transness is and what isn’t, we would have to include people that aren’t really trans."
The writer has missed it. The metaphysical issue is, as I mentioned above, that meaning is fundamentally metaphysical. This can be inferred from the work of Gödel (no closed systems); but it's intuitively sound as well. If all definitions are circular, then no definition has meaning; thus, if there is meaning, it comes from a metarational source.
Nobody knows what makes us transgender.
Let me repeat that: Nobody knows what makes us transgender.
And this necessarily means that claims of requirements for being transgender are merely speculative. Dogmatism is simply ridiculous; it's like arguing about religion.
I am more than a little confident that the reason that this issue is so important to the writer is its political consequences; and I sympathize -- of course, I sympathize. I live in a Hate State. But we will not solve any problem by throwing reason away. Gender must be objectively real, else we are delusional; and, being real, it has limits. There is a boundary between what it is and what it is not. We may not know the precise nature of that boundary; but that is a very different thing from saying no boundary exists.
Nominalism is a philosophy of meaninglessness and despair. Uncertainty is an uncomfortable fact of life, but sacrificing reason to escape it is self-destructive.