Accurate facts here
Semenya officially for sure has 5-ARD-type 2, normally functioning testes and XY chromosomes
Chand also has XY chromosomes and testes but there is no official document on her intersex disorder, however it is stated to be AIS.
Most athletes with AIS have partial, not complete AIS, and it's likely Chand does too.
Athlete with C/PAIS do not produce female levels of oestrogen so will have less body fat and may be taller than normal women, since oestrogen fuses bones during puberty.
No athlete with PAIS will gain the full male benefit of testosterone, which Caster Semenya, and male athletes in general , do.
So you are unlikely to end up with PAIS athletes dominating to the extent of 1-2-3 as in the 800m with 5-ARD. Of course PAIS is a continuum and the P part is not quantifiable, so some people with PAIS are just slightly under virilised males, and not in any sense female.
So there is potential for people with cases of PAIS that would normally subjectively be deemed 'male' to end up in women's sport, and such athletes would essentially be no different from transgender athletes in that they would have been born with penises.
I am not sure if it is possible to 100% determine that androgen insensitivity is complete or merely partial, but my understanding of the situation is that for CAIS there is infertility and the testes are likely to become cancerous.
Also with CAIS there is no possible gender assignment other than female - you don't process testosterone at all, and because the testosterone cannot be used, it ends up being converted into oestrogen and resulting in breasts etc. This is the same process by which oestrogen is produced in normal women in that the ovaries synthesise hormones which are converted into testosterone and then into oestrogen. Chemically speaking oestrogen (or rather its most potent form, estradiol) is just a single reaction, with an enzyme found in many parts of the body, away from testosterone.
So it is for example medically possible that someone with CAIS or PAIS might remove their testes, but they would not necessarily do so, and if they did it might result in needing to take oestrogen supplements as the removal of the source of testosterone results in low oestrogen.
There are some people who insist that women with CAIS are actually men, which is simply wrong in that even though they have testes, they do not process testosterone at all, so whatever effects testosterone has on the brain(and it does) does not happen to women.
I'm pretty sure that Dutee Chand has PAIS and there is some possibility that testosterone has influenced her sexuality, but that same possibility might apply also to women with with ovaries who have high testosterone levels, so there isn't a 'she likes women so she must be a man' gotcha here.
I think that women with PAIS are overrepresented in sport but I am not sure that they should be excluded.
As far as Semenya goes it is quite complicated in that Semenya probably performs exactly as well as a man would, BUT there are far more men in the world and it seems that CS is not good enough to win with female.circulating levels of testosterone.
I would say:
5-ard-2 - normal testes, normal T - compete as male
17β-HSD III - testes don't convert precursor into T properly, so T could be very low resulting in female phenotype - probably compete as male, but perhaps if it can be shown that the athlete's body is not virilised then they could compete subject to 2nmol/l T
CAIS - should be allowed to compete as female without restriction
PAIS - ? see virilisation arguments above and T below 5 nmol/l
Essentially in any case where an athlete has been born with testicular tissue and processes androgens then there needs to be a process whereby those who are virilised are excluded from female sport and those who are not virilised can compete. This should apply also to trans, so that those with normal male bodies such as Rachel McKinnon can never compete as female