That started well.
Gender is not sex. It's a product of time and culture, not innate. It's a ridiculous patriarchal construct and forcing people into boxes based on superficial personality differences is oppressive, regressive bollocks. Yes! (Of course, claiming to be in the other box based on those same superficialities is equally regressive, and acts to reinforce the boxes.)
Para 5 - who is this 'we'? It's certainly not gender-critical feminists, who still want to smash the boxes, as our feminist foremothers did.
Sex-based rights are indeed based on sex. And for good reason. Enforcing them is not resteicting people's rights because of their gender, it's protecting them when they have a need because of their sex. They don't just affect trans people, or trans and 'intersex' people. They affect (and protect) everyone - because we all have a sex.
'Intersex' is misleading, and generally considered offensive. It was replaced 20 years ago by 'differences of sex development'.
Everyone with a DSD still has a sex. They are not somewhere inbetween. Indeed, the vast majority of DSDs are sex linked - only people of 1 sex can get that spexific type of DSD.
The proportion of people with a DSD is not 1.7%. The study that gave that figure has been repeatedly debunked, and included all sorts of illnesses related to the reproductive system or sex characteristics that nobody would consider to be DSDs (things like PCOS or endometriosis are not DSDs) as well as very minor malformations of the genitalia. It would be like claiming x% of people are not bipedal and counting those born with an extra toe.
People with DSDs and the organisations that represent them have repeatedly asked to kept out of the trans debate because there is no link between the 2 (the Tavistock originally screened everyone presenting to the gender clinic for DSDs; they stopped because there was no link).
Sports are not gendered, they're divided by sex (or were until they recently tied themseleves into ridiculous knots because they had forgotten why they are divided that way). This is almost always because men and women have different biological limits.
In a very small number of cases (including chess) women are not at a physical disadvantage but do face higher social barriers - this is a result of gender, but the solution is not to divide competitions by gender instead of sex - it is to eliminate those barriers. And then have mixed sex competition (but it does have to be done in that order).
Semenya does have a DSD. One, as PPs have explained, that only affects men. And should therefore not be included in women's sports.
Dividing most sports by sex-blind physical categories is simply not possible. There are too many variables. It's not just height and weight, but lung capacity, proportion of fast-twitch muscle fibres, grip strength, skull thickness, bone density, Q angles ... and endless other things that still differ even in men and.women matched for overall size. You'd end up with categories of 1 person each.
Refuges/prisons divided by sex, children are children, men don't have periods. Yes - we're back in agreement there.