No need to despair just because I don't agree that your story is obvious. Aren't you being racist (and probably classist, to boot) to suggest that poor people everywhere will be unlikely to have easy access to DNA testing unless or until they are at the top of the sporting tree? Look at how many British people went onto Jeremy Kyle to get a DNA test to prove or disprove the paternity of their babies. If they were readily available to all people on all incomes, that wouldn't happen, surely?
Are you suggesting that athletes are tested as a matter of course at lower levels? TBH I don't have a clue, but I doubt it is left to the individual to sort it out, and it seems unlikely to be insisted on at local level. They will happen in supervised conditions, by the authorities at higher (International?) levels, or what's the point? Tests will be imposed, probably free of charge to the athletes, who in any case will have had to afford the flights, passports and so on, or be sponsored in some way. They will be applied equally to people of all colours and creeds, and someone who genuinely believes that they are female will be surprised, whatever colour they are, and however developed or otherwise is the country of their origin. Nothing racist about it.
You really are wandering into fantasy land in your determination to make a case for male-bodied people to erase women from sport😂. That's bad enough, but your suggestion that anyone who disagres with you is racist is scraping an already very well scraped barrel.