What you did in your hypothetical is to point to a (theoretical and unspecified) safety concern NOT related to sex, and complain that sex category didn't remove it. You're applying an impossible standard: you demand that when sex category is established, then no safety concern must ever present for any reason ever, even theoretically.
We don't expect that standard from any other measure.
Yes, sex testing would mostly affect female sport, that's true.
No, for nearly all athletes, except only for the very rare cases where more diagnostics after screening is required for health reasons anyway, it's a cheek swab. This is not invasive.
> trans people don't just all agree to be trans
Well some people with gender dysphoria are in denial, and others choose not to live it out externally (i.e. present as the gender they believe they should be). One of the main tenets of transgender ideology is that gender identity is determinate of whether one is a man or woman, which is something that anybody can choose to believe or not believe.
> the claim was that trans people are being killed, and I provided stats that show this to be true.
No, your argument was:
> Also statistics are absolutely clear that conservatives are murdering trans people
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