Though the epistemological means through which one's gender identity is often erroneously directed solely at transgender persons, I think --- as a cisgender person --- that it can uniformly apply to me and other cis persons.
A common critique of transgenderism is that is metaphysically untenable as it predicated on a highly subjective and thus dangerous predicate: that is, it is often believed that the only way whereby one can ever know of what gender identity one is part is by listening, so to speak, to one's emotions, to one's feelings, by assessing one's own private, subjectively-known psyche-psychology which is inaccessible to persons external to oneself.
If, some trans critics assert, the masses were to accept what the transgender community at large, in some people's estimation, espouses with regard to the framework by which one discovers the gender identity of which oneself is part, no one would be able to know anything with regard to external selves' gender identity. The gender identity of external selves would literally be unknowable. The only framework with which one would have to work with regard to the discovery of the gender identity of external selves is, essentially, guesswork, the process of elimination, or by asking the agent themself with what gender identity they identify and as what and in what way they wish to be addressed when one refers to them.
Because of the reasons mentioned, some trans critics say that the most reliable and great form of epistemology with regard to a person's gender identity is the very body into which they are born, the body in which they are embodied. It is the body which one possesses which defines everything about oneself: with whom one ought to have sex; the gender-based activities in which one ought to partake; the clothes which one ought to wear and the like.
For one to say that one "feels like X in Y's body" is poor epistemology and, most probably, a sign of a very serious mental health and or existential issue according to the trans critic. It seems to, in their estimation, promote a very solipsistic mode of knowing or discovering things --- by 'solipsistic' I mean that it is only one's own gender identity of which one can be absolutely sure --- or at least more sure in comparison to that of others --- sort of like how the solipsist insists that the only thing of which they can be totally sure is that it is they and their mind who exist.
So, my question to you is through what --- to use the trans critic's word --- (objective) epistemological means can one discover the gender identity of oneself and other selves? Does one need to undergo a brain scan to see if one has the sexed brain (if such a thing is believed to exist) of the gender with which one identifies? Does one just need to accept that one is bodied in the way that one is and the problems which one has with regard to what is believed to be one's brain-body or mind-body or soul-body --- it differs because each person, of course, believes that one is the way one is because all people subscribe to different axioms --- mismatch needs to be overcome in non-surgical, non-hormone-taking, therapeutic ways which leads to one's accepting one's body wholly or predominantly? If one's mind and or soul and or spirit is believed to be separate from one's person, how is one's gender identity objectively discoverable?