"if in the future particular mutations or combinations of mutations could be reliably linked to (childhood gender dysmorphia or to autogynephilia, then that would be worth knowing, it seems to me)..."
The thing is, this is a bit of a lost cause, in my opinion (as are studies into the "genes for" intelligence, for example).
Here's an example of an issue that could come up. In this hypothetical example, let's say there are no "genes for" dysphoria / autogenephilia. It's all environmental. Nevertheless, we will expect to find genes that are reliably linked to these disorders.
Here's why - imagine there is a rare dominant gene which causes male individuals to have strongly nurturing aspects of personality. In the context of patriarchy, nurturing males are abused by men for violating patriarchal rules. Much of this abuse will be specifically mysoginistic and homophobic abuse "what are you a p***?" A subset of these abused individuals will associate this abuse with their the male sex, wish they were female so they did not have to experience such abuse and could just "be themselves", and will begin to despise their own bodies. Years go by, and the result of a genetic study would find that there is a very strong enrichment for this dominant gene among individuals identifying as Transgender. Although the gene simply impacts personality - not transgender identity per se - it will be announced in the media that scientists have found the "transgender gene"!
Now, imagine the same gene exists in a genderless utopia. In this non discriminatory environment the individuals are free to express their nurturing aspects of personality, and are praised and supported in this. They feel very comfortable in their skin and contribute successfully to society. They do not have any psychological to be seen as female as they were never exposed to misogynistic or homophobic abuse for being male.
Obviously it's a cartoon example but it illustrates the major issue in behavioral genetics. You can't control for gene by environment interactions until you have a utopian (or at least non-patriarchal) environment to compare to. Of course there COULD BE "genes for" autogenephilia and sex-based dysphoria. But we can't distinguish them from the above until we have a utopia to compare to. Which we won't have.