Re, this earlier point of yours:

However, if somebody has the chromosomes, external genitalia and socialization of the opposing sex

If you look more closely at the drawings, photos and descriptions given in studies of the genitals of those whose external genitalia might have appeared to be ambiguous or similar to/the same as the opposite sex upon cursory visual examination at the time of birth, I think you'll find that it really isn't the case that people with DSDs are born with the "external genitalia" of the opposite sex.

If it were the case, it would mean there are some DSD females born with penises and testicles, and some DSDs males are born with labia minor, labia minor, vaginas, clits and female urethras located in the vulva as female urethras are. But this is not really what happens.

On closer examination through eyes that more informed about the details of human anatomy, particularly female anatomy, what's often thought to be a penis in a female baby at birth is actually just an enlarged clitoris (known as clitoromegaly); and what might be mistaken for a scrotal sac is fused labia.

Similarly, in XY babies with DSDs that affect the external genitalia what's often mistaken for a vulva at birth is often empty scrotal skin/sacs into which the testes did not descend. And what gets referred to as - and is assumed to be - a "vagina" turns out on closer examination to be a blind, shallow pouch of skin inverted into the pelvis that has none of the properties of a vagina.

In the case of full-grown XY adults with 5-ARD, the papers I've read say the internal pelvic skin pouches that get mistaken for vaginas are usually under an inch in depth, and may just be a dimple. In the case of XY adults with CAIS, the skin pouches called vaginas tend to be longer, in the range of 2.3 inches. But that's still much shorter than the vaginas of XX females, since the "average" adult human vagina is said to be 3.7 to 7 inches in depth.

Aside from the depth, there are many other ways in which the "vaginas" of XY people with DSDs that affect genital development differ from actual vaginas. After all, a vagina is not just an indentation or hole in the groin made out of skin. A vagina is a muscular, highly elastic tube with its own unique, self-lubricating lining of special self-cleaning mucosal tissue that contains zillions of proton pumps and sustains its own unique flora. Functionally, too, a vagina is more than a hole to stick dicks into - though a flaccid hole for fucking is the way it's typically regarded in a male-dominated, penis-privileging porn culture. The vagina evolved to function rather brilliantly and miraculously in its core role as a birth canal with the stretchiness, strength and muscular force capable of propelling new human beings into the world. Since humans develop unusually large brains and heads in utero, the stretchiness and strength of the human vagina in childbirth is nothing short of miraculous, as is the amazing (albeit painful) expansiveness of the human cervix too.

In persons with 5-ARD specifically, the urethra often empties into the shallow skin pouch, which gives the appearance that XY people with 5-ARD "pee from their vaginas." Peeing from the vagina, in turn, is often used as "proof" that males with 5-ARD have female external genitalia. Semenya, in fact, has used this very explanation to bolster Semenya's claims of being female. But, of course, what such claims really show is ignorance of actual female anatomy. The fact is, females do not pee out of our vaginas. Our urethras do NOT empty into our vaginas, they are entirely separate structures to our vaginas - the openings of the two organs are adjacent in their placement in the vulva, but the female urethra and vagina are not connected.

If you look into DSDs and their history, you'll find that in the majority of DSDs babies are not born with with external genitalia that look ambiguous or truly resembles the opposite sex; this happens only in a tiny number of DSD conditions. You'll also find that in the past, and in some places still today, all sorts of anomalies in the appearance of male genitals that have nothing to do with DSDs and do not impair male reproductive functioning and gamete production long have been erroneously classified as "intersex" conditions. This includes having a very small penis known as a micropenis, having undescended testicles, and having a malformed male urethra that empties out the side, underside or top of the penis rather than through the tip (hypospadias and epispadias).