I think there are several arguments on this thread that are getting mixed up.
Firstly, there is the argument about Caster Semenya's physiological makeup. I have seen posts on this thread that:
-Caster is a woman with high levels of testosterone or
-Caster is a person with a vagina
That is incorrect. Caster Semenya has the DSD 5-ARD, which is a disorder of male sexual development. She has XY chromosomes and, due to the nature of her DSD, went through a largely normal male puberty.
I'm not bothered about whether Semenya extracted sperm to biologically father her own child. However, it is relevant that other people with the same disorder are able to do this, as it demonstrates how unequivocally biologically male people with this disorder are - regardless of their personal gender identity or how they were raised.
(That's very different, for example, from people with CAIS - complete androgen insensitivity syndrome, who are also genetically XY and have male levels of circulating testosterone, but are completely unable to respond to it at a cellular level, so develop a female phenotype and female secondary sexual characteristics at puberty, but are sadly infertile and have no ability to have biological children. People with CAIS are able to compete in female sport and do not have to lower their testosterone level, because their body just doesn't respond to it. Dutee Chand is a good example.)
The second argument comes about when most of this information about Semenya's phenotype had been explained. Then the argument switches to being about gender identity. There is a strong narrative pushed in the media that Semenya was raised as a girl; that she had no idea that she wasn't a girl until she had to have a genetic test as an adult; that she just wants to be able to live her life quietly as a women; and that it would be cruel to deny her sporting success in her chosen gender identity.
That's when the arguments about how she was raised etc come in. I agree with a previous poster that these are less relevant: much as it feels unfair at the individual level to Caster, she should not be allowed to continue to compete in women's events, because she is biologically male and went through a normal male puberty.
However, if arguments are made that Semenya should be able to compete as a women based on her gender identity, it's worth exploring what that gender identity is. There's not much evidence available, but if her family use male pronouns for her, she wears traditional male attire for e.g. her wedding, and people at her school assumed she was a boy, that overall suggests that she has a male gender identity.
Now, I agree that clothes, pronouns and stereotypes don't change someone's sex. But if the argument is that Caster Semenya should compete as a woman because gender identity is more important than biology, it would be good to see some evidence that she feels she has a female gender identity. If the argument is that all this is crude stereotyping, we're back to just the biology argument.