Can I offer a round up of the science? (Since I'm presuming that no-one wants to trawl through a million and one internet links - but FWIW I find Joanna Harper, one of the scientists who advises the IOC - to be clear and open to discussing the pros and cons. Full disclosure - she is trans, but describes herself as "scientist first, athlete second, trans after those", and as far as I can tell, cares very much about the underlying principle that sport should be fair).
There was a big survey of female athletes done about twenty years ago. Non-intersex women typically have testosterone between 1.5 and 2.5 nmol/litre, but there are some outliers. The men's range is between 10 and 30 nmol/litre. To deal with outliers in the distribution, the upper limit of the women's blood levels was set at 10nmol/litre, the bottom of the naturally occurring men's range. This is 5 standard deviations from the mean of the female distribution. The IAAF then adopted a rule which said women (including intersex women) had to take androgen blockers which brought their testosterone below 10nmol/litre. (In some cases this can be something as relatively non-invasive as contraceptive pills, in other cases intersex women were pressurised into having gonadectomies, which I think is unacceptable).
There is a further complicating factor in that you don't just have to have testosterone in your blood, you have to have androgen receptors in order to make use of it to build excess muscle (excess relative to normal female levels). And intersex women can have either partial androgen insensitivity syndrome, PAIS, or complete androgen insensitivity syndrome, CAIS. Intersex women with the former will typically have body shapes visually closer to men - flat chests, male-looking musculature. Intersex women with the latter have typically female looking bodies and musculature. However, "looks like" isn't and shouldn't be the issue. (I'm old enough to remember the "is she really a man" furore over Kratachvilova. My suspicion, and that of most other people, would be that she was doping, probably with testosterone, but she definitely wasn't a man or intersex because she later went on to have a child). The issue is whether this gives these athletes an actual performance advantage, and if it does, whether that's any different to any other sort of naturally occurring variation.
Now quite rightly, none of us know the details of Caster Semeya or Dutee Chand's medical notes, and rightly so - they deserve to have their medical confidentiality respected. But what it is thought happened is this: in the early part of her career, Semenya was made to take androgen suppressors in line with the IAAF rules at the time, at which point her times dropped from world beating to somewhere in the chasing pack. Then Dutee Chand (who is thought to have CAIS) took the IAAF to the Court of Arbitration in Sport (CAS) and won, on the grounds that her actual blood testosterone levels were irrelevant if she had no receptors, therefore she should not be forced to take unecessary medication. This led to the two year "let's see what happens and do some further study" period where the maximum testosterone levels were relaxed.
I happened to watch the men's decathlon 400m just after Semenya's semi-final for the 800m last night, and was struck by how fast these non-specialist 400m runners were. For reference (I just checked) the four fastest men home in last night's decathlon final are all faster than Semenya's PB for the 400m. Semenya is fractionally faster (by about 2 or 3m) than the women not causing any suspicions, but wouldn't be anywhere in a field of world-class male specialist 400m runners. She has maybe a 1% advantage over the other competitors, but not the systematic 10% or thereabouts difference between men's and women's record times in running that we see at all distances from 100m through to the marathon. So we're back to the question of "is this natural advantage, like Phelp's hand/wingspan, or Bolt's incredible metabolism, or is it unfair?"