Well, I guess it first of all depends on the sport. I don't think it will matter a lot what gender your opponent is in the world cup chess, and in horse sports men and women are already part of the same competition.
What it comes down to is that that it's a scientific fact that the average woman can hold less oxygen in her blood than the average man, and due to this men can normally hold out longer, and quite often men also have more muscle. This is average, but it is proven to be the case. The split up in sports is based on this. And the sport korfball is even unique as teams are there half male half female, however male players may not block balls thrown by female opponents nor vice versa.
Now it comes down to the science part to see if this is fair, so not about the social part or possible sexism, just the science. That it can only be fair if all competitors have the same advantages and disadvantages coming with their gender. The question is in how far this is the case for a man who became a woman.
From what I know about transsexuality, even spoken to a man who was in the process of becoming a woman, it's more than just dressing in the other sex' clothes or just the removal of a p**is replacing it with a va**na. Actually that operation is (odd as it sounds) the least heavy part of the process. You go to a giant hormonal treatment in order to let nature do as much as possible. These hormones will cause a man to grow boobs like women have, so they are semi-natural. This being said, I only deem it logical (although an expert in this field will have to confirm this) that a man grows weaker physically in the process as well. If that means the man who became a woman comes out physically the same as a woman who always was a woman from the start, and yes if my hypothesis is scientifically correct it would be fair, since the advantages of being a man should technically have been removed.
A similar discussion came with a woman who was a woman but was in hormones almost a man, and who had to take drugs to break that down as it was unfair as other women would need to take doping to be as strong as she was. Seeing as these drugs would weaken her and make her more equal to the other women, it only makes sense these drugs would have the same effect on men.
However what sounds logical and what actually is logical are two different things and sometimes completely unrelated, so I need a real scientist specialized in this field to back my theory up.
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