My favorite is "fact" three. It's hypocritical when they bring up gender policing when they're the biggest enforcers of gender stereotypes.

Also, in sports, particularly competitive sports, policing of athletes' bodies in various ways comes with the territory. In elite level sports and various professional leagues, anti-doping regulations require that athletes get randomly visited and called upon to drop their trousers and undies and urinate in full view of a sports official so that their pee can be tested for banned substances.

In sports where there are different categories based on weight, such as boxing and wrestling, athletes are weighed publicly. In professional boxing, the weigh-ins long have been a media spectacle, as this clip showing Cassius Clay/Muhammad Ali talk trash about Joe Louis and Sonny Liston at a weigh-in from 1964 shows: https://youtu.be/SJRHxr1fYw0

Take any sport, even many JHS and HS scholastic sports, and there's probably a website or many where you can look up the stats of individual athletes, which include not just records of how well they've performed, but personal information such as their height, weight and sometimes their shoe size.

For 30 years starting in the mid-1960s, elite athletes competing in the female division were all required to give buccal swabs of saliva (from inside their mouths) in order to get their sex chromosomes tested. This practice was discontinued coz of complaints and legal challenges by athletes competing in female sports found to be XY. Buccal swab testing - which took a few seconds, was painless, did not involve disrobing or bodily probing, and only had to be done once in an athlete's career/life - did not engender [LOL] a hue and cry from XX athletes. The XX athletes did not mind this one-time "policing" of their bodies to ascertain their chromosomal sex. All the athletes who raised formal objections were ones that the sex chromosome testing revealed to be XY.

Significantly, the first XY athlete to win a legal challenge to the practice of buccal swab sex chromosome was on the Olympic Committee that in 2015 decided to allow male athletes who "identify as" female to compete in the Olympics so long as they've lowered their testosterone to levels lower than the normal male range, but are still four to 10 or more times higher than the female range.

Those who make the "gender policing" argument like to bring up the specter of what happened before DNA testing became possible and the various DSDs began to be described and well understood in medical literature. In the 1950s and 60s, elite athletes in the female category in some elite international sports, such as track & field, had to provide medical certificates documenting their "femininity" and to strip naked and parade in front of sports officials. The athletes found this invasive, degrading and sexist - understandably so, coz it was. But all of that ended with the introduction of sex chromosome testing in the mid-60s.

Still, males who want to compete in female sports and those who back them still continually call up the specter of the kind of sex testing that was stopped more than a half century ago to make the claim that all/any sex testing in today's era and the future is inherently unfair, sexist and prurient - indicative of a voyeuristic, fetishistic, perverted and entirely uncalled-for curiosity about "what's in someone's pants."

Caster Semenya's PR campaign and legal case heavily exploited what was done in to female athletes in the past as justification for why no one in today's era should be allowed to raise questions about Semenya's sex - which the detailed CAS court decision released in 2019, and statements from the IAAF/World Athletics, make abundantly clear is male. TIMs and those arguing on their behalf employ the very same reasoning. Today the injustices done in the past to XX athletes across the board are being appropriated by, and on behalf of, XY athletes - both "trans" and with particular male-only DSDs - who insist it's their right to be included in female sports so long as they "identify as" girls/women.