It's a bit more than that.
First of all, there is no doubt that they are male. The female category excludes males, including subsets of males who are disadvantaged in some way compared to others, on the basis that the average male has an athletic performance advantage over the average female.
CAIS athletes are very significantly overrepresented in elite female sport in relation to their incidence in the general population. (Source: Emma Hilton, who agreed with CAIS inclusion in female sport.) This implies an athletic advantage which can only be due to being male, since they are subjected to female socialisation and only have the limited opportunities which are available to women and girls.
I am not a scientist but it seems to me that a male with CAIS cannot be totally insensitive to all androgens if they have internal testes which produce testosterone. They can't utilise the testosterone, but females with CAIS do not develop testes, so clearly there is a difference there.
Just because we don't know why they have advantage is not a reason to ignore it and make female athletes pay the price. I don't think the approach should be that CAIS athletes should be allowed in female sport unless and until we discover why they have a small athletic performance advantage - it should be the other way around, if anything. Otherwise it's unfair on women and girls.
The resources and opportunities available to female competitors are tiny in relation to the riches which males enjoy. So again, unfair to make females share these with males who will disproportionately benefit from the best opportunities, top prizes and accolades because of their male advantage.
There is also a lack of reciprocity. Females with DSDs which give them an apparently male phenotype do not carry an advantage into men's competition.
Resources are finite. Only 8 sprinters can make the final at whatever level. And for every CAIS male in the female category, a female misses out. That's unacceptable.
Athletes whose results are flagged up after screening undergo further investigation. Some of them are found to be female. All well and good. CAIS athletes are male.
The reason for the female category is to exclude male advantage and enable women to compete on a level playing field. Eligibility for female category should be based on sex, not on whether an individual or group could be competitive against men.