So, I went off looking for evidence of this claim:
*"Occasionally, the hormones that trigger the development of biological sex may not work properly on the brain, reproductive organs and genitals, causing differences between them. This may be caused by:
additional hormones in the mother’s system – possibly as a result of taking medication"*
since the page helpful provides zero citations, and found this 2015 paper Early androgen exposure and human gender development which "critically reviews the available evidence regarding influences of testosterone on human gender-related development". It covers research which links or fails to link sex stereotyped behaviour in children to prenatal androgen exposure. Some studies find a high correlation, other find non at all. It also covers the findings of one research group which "looked at the correlation between amniotic fluid testosterone and a range of characteristics related to ASD" saying that "These studies also merit careful examination, because they are widely cited to support a contribution of early androgen exposure to ASD."
Concludes:
"Thus, although a primary basis for interest in understanding the influences of testosterone on human behavior has been the idea that androgens might contribute to discrepant sex ratios for psychological diagnoses, research in this area has been relatively scant for disorders other than ASD, and for ASD has ultimately produced findings that do not support a contribution from prenatal testosterone exposure. This lack of research, and even the lack of clearly supportive findings, might reflect, in part, the rarity of individuals with both atypical androgen exposure during early development and a gender-linked psychological diagnosis and the lack of a powerful measure of prenatal androgen exposure in individuals without hormone abnormality."
and
"The relationship of finger ratios to prenatal androgen exposure appears to be too weak to be useful in studies attempting to relate prenatal androgen exposure to later behavior [9,16,17], and this review suggests that this may be the case for testosterone measured in amniotic fluid as well. Although one research group has found predicted relationships, others have not. Small sample sizes may have contributed to the failures to find significant effects, but the insignificant correlation that has been reported between testosterone in fetal blood and testosterone in fetal amniotic fluid [55] also does not support the robustness of the amniotic fluid approach."
So, no clear correlation between prenatal Androgen exposure and gender identity disorder, and no clear causal link between either of those things and ASD.
OK, so I went to take a look at the contributors and found Professor Melissa Hines of Cambridge University. In 2011 she spoke at the "woman's word" festival in Cambridge arguing that
"The overall conclusion, based on all these types of research, is that children’s toy preferences relate to the prenatal hormones they were exposed to. Not only do boys tend to play with trucks whereas girls tend to play with dolls, but within girls, those who are less interested in dolls and more interested in trucks tend to have been exposed to higher levels of testosterone during gestation."
Her key publication that she lists is “Prenatal hormones versus postnatal socialization by parents as determinants of male-typical toy play in girls with congenital adrenal hyperplasia” coauthored, amongst others, by Vickie Pasterski. In fact, she authored at least 10 papers with Vickie Pasterski.
Does that name sound familiar? That's because she was the expert witness called upon to over rule social services on the transitioning foster children and in Jay vs Secretary of State for Justice -- getting a GRC on appeal after panel says 'no' three times
So, I think this would merit further probing.