I am not sure what you mean by ability.
I'll take a stab at the others, but boxing might be a real good example. Tell me, what is the difference between a women hit with 100 lb of force by another woman, and being hit with 100 ls of force by a man? Is there a difference? Does one's ability to withstand a given amount of force in a blow make a difference? Number is made up for example's sake, and if unrealistic, then substitute in any given reasonable number.
Women already do better in long term endurance races to start with. However, have qualifying runs where people who fall within a given range for the distance compete against each other. Sex doesn't have to be the factor there.
There is more to these sports than I would be able to analyze for such. This is definitely where the experts should come in. I'm going to doubt any such exist on this forum, save the arm chair experts we hear from too often.
This would probably run along the same line as boxing. If you have two people of equal strength, then it all comes down to skill. Granted, with sufficient skill, one can defeat a stronger opponent, within a reasonable range. And if a person wants to challenge up a level, they should be allowed, whereas one should never be allowed to challenge down, which is not the same as accepting such from below.
Granted that some sports should not be divided at all. Did you know that skeet shooting in the olympics used to be a mixed sport, until 1992 when a woman won the gold, and then suddenly women were not allowed to compete until the 2000 Olympics in their own separate category?
Again, I want you to keep in mind that I am not saying that a given women is likely to beat a given man, or female and male if you prefer, in many sports, although there are many in which there is no difference. I am saying that by making a different criteria other than sex/gender, we will have a natural separation of the sexes (regardless of gender), while also allowing for any exceptions to compete with others on an equal playing field.