There are categories for those who are too small or not good enough in some sports. Boxing, rowing, judo all have weight categories. Weight lifting has competitions where your body weight is a factor as well, probably loads more. Edit: football with under 21s or sports with veterans categories.
For men who transition into women there are rules. I believe the main point in them at the moment is to cap testosterone levels. I don't think anyone is particularly pleased with them as rules, but they are reasonable and I haven't heard any better suggestions.
Competitive sport is slightly different from Opera, rubbish singers just won't get employed. But it's not ok for Pavarotti to take part in a childrens talent show and take first prize.