If your only criteria for deciding whether or not a person can compete is based upon gender lines and they fit that criteria, its only fair to let them compete.
More In Depth Thoughts In No Particular Order
Different athletes have different body types that allow them to perform better or worse in certain sports. For example, if someone with the body of a horse jockey wanted to play basketball, by all means they should play, but it's unrealistic to not realize they're gonna have a significant disadvantage. Similarly, if someone who has the body of a linebacker wants to take up gymnastics, by all means, let them, but realize that they're gonna be at a disadvantage, albeit for different reasons. There's more to a physical edge in sports than just body shape. Like the runner above, sometimes those edges are based in hormone levels. For others, there might be psychological advantages or advantages in pain tolerance or endurance or what have you. If someone has a natural edge for one reason or another, it's not fair to say "nerf your edge or you can't compete." Athletes can either lag behind, keep up, or excel. That's the whole point of sports.
Know what's often acknowledged as an edge but rarely talked about? Money and time. Someone who has the money to hire private trainers and physicians, better equipment, better diets, and so on, is gonna have an edge over someone who doesn't. Someone who has the free time to devote thirty hours a week to training is gonna have an edge over someone who can only train for five hours a week. There's a reason professional sports teams dump crazy amounts of time and money into their athletes. If they don't, they're not competitive. Period.
I'm all for having more granular distinctions for competition when it makes sense. Sports like Boxing and MMA have weight classes for two big reasons. Partially it's because if you put a welterweight and a heavyweight in the same ring, it's understandable that the fifty pound weight advantage the heavyweight has is pretty much insurmountable. It's literally not a fair fight. More importantly though, it's a huge safety issue. The welterweight, no matter how good they may be, could get seriously, seriously hurt. But for a lot of sports, that doesn't make a whole lot of sense. Are we gonna start dividing up basketball teams into height classes? Are we gonna divide baseball into age classes? Probably not. Why? Because there's just not a compelling reason to.
All of that said, this isn't a black and white issue, as stated in the article. Part of the philosophy of athletics is that things are supposed to be as fair as possible and that athletes shouldn't be unfairly impeded or given an unfair edge, that they should win on their own merits. But as with everything in life, nothing is ever completely fair, and trying to figure out what is and isn't fair and how to balance those things out, will always be tricky, should always be considered and reconsidered and re-reconsidered critically, and will never, ever completely erase that some people will have more of an advantage than others.