CS clearly considers herself female, but she just as clearly is not. Instead, she is a human who is genetically male but with a fetal developmental defect leading to female secondary sexual development (which also includes mental aspects and thus female sexual self identification as a consequence of this female mode development).
In contrast, the development of her musculature especially during since puberty did not follow this female mode. Instead, her muscle cells are apparently sensitive to the testosterone produced by her testes. To note, she improved from an 800m time of 2.04 to 1.55 within nine months around age 17, which in fact triggered the initial sex test of 2009 (such a change is either a sign of massive doping, or the puberty related changes typical for male development).
While for most fields (social, legal, etc.) CS’s status as a woman must not be questioned, it therefore makes no sense to do so in sport: The relevant part of her physiology is, like her genetic makeup, male. Thus, she should be treated as a good but not international level male athlete rather than the world’s outstanding female runner.
She is not unique in this, e.g. the two other medalists of the 2016 Olympic 800 m race are both also either known or strongly suspected to have the same condition.