I understand that the claim is that because she was born male she has an advantage. I'm asking specifically what advantage is being claimed.
The typical cismale will put on 15-20kg of lean mass from 12 to 21 even if all he does is sit around playing Call of Duty and masturbating five times a day, as many do. The cisfemale in that time will put on about 5-7kg of lean mass, she will gain much more fatty mass. If either of them are physically active in that time in a way that challenges their muscles and bones, such as lifting or contact sports, the mass gain will be greater. If they are the kid who faked a stomach ache to get out of PE class and who goes through a vegan or eating disorder phase, the lean mass gain will be less.
Having been through a masculine adolescence provides a lasting advantage in muscle and bone mass. Obviously given normal human variation in size and athletic ability this will not be universally so - a 5ft narrow-framed cisman will probably lose a wrestling match with Serena Williams, let alone if that cisman becomes a transwoman. So we're just talking trends.
Likewise, a person who uses anabolic steroids will see significant lean mass gain, and much of this will remain even after ceasing steroids. So if we are to deny that having been through a masculine adolescence provides a lasting advantage, by this reasoning a ciswoman should be able to openly use anabolic steroids for several years, stop, and then compete in drug-tested sports. I think you would find that WADA would come up with a way to stop that. Now, if you want to say that testosterone does not give a lasting advantage, then you had best have a word with WADA, because they're spending a few hundred million dollars a year testing for its exogenous use.
At the moment there is a fairness issue in sports, because of inconsistent standards. Given the normal range of ciswomen's testosterone is 0.2-2.4nmol/dL, if a ciswoman tests as having 5+, this is taken as a positive doping result, and further tests are done to determine if she has been using exogenous testosterone. However, transwomen are allowed up to 10. This is interesting, because it varies by country, but basically if a cismale tests at 8 or under, this is considered a medical condition requiring exogenous testosterone. So the transwoman athlete is allowed to have testosterone levels higher than some men have naturally, twice as high as ciswomen are allowed to have, and 4-50 times as high as most ciswomen will naturally have.
Cismale natural testosterone levels = 8-40nmol/dL
Cisfemale = 0.2-2.4
Cisfemale positive doping result = 5+nmol/dL
Transfemale positive doping result = 10+nmol/dL
The reason transfemales are allowed higher levels is that while upon hormonal treatment they drop to 10 or under within a couple of years, it typically takes 10+ years (and the removal of the testes) for them to get under 5nmol/dL. Extraordinarily few people can keep up a top athletic performance for 10 years without competing, add in the emotional and social turmoil most transwomen will suffer during transition (as with any life change), and consider that most don't transition till after adolescence, so by the time it's all done they're in their 30s and past their athletic prime - this means that holding transwomen to the same standard as ciswomen would essentially exclude transwomen from open competition, though there'd still be a place in master's competition.
Thus, when considering transwomen and ciswomen and competition, there are basically 3 choices,
1. holding transwomen to the same standards as ciswomen, effectively excluding them from competition
2. allowing different standards to get transwomen competing, leading to unfair competition
3. allowing ciswomen to dope up to 10nmol/dL to match the transwomen
Nobody is going to allow open doping, which removes #3 as an option. So in the name of inclusiveness, the IOC and others are allowing unfair competition against ciswomen. You don't hear many ciswomen athletes speaking about this because they've been gagged; at the time Laurel Hubbard was competing, members of the Australian Weightlifting Federation were told that if they spoke about it publicly they'd be expelled from the federation.
To my mind it's like older athletes and TRT. In sports, there are some drugs which are performance-enhancing, but which are also treatments for genuine medical conditions. Obviously these medical conditions hinder performance, and the medicine is designed not to enhance performance, but remove the hindrance. For example, asthma inhalers. So sportspeople can get a TEU, a therapeutic use exemption. This is why a remarkable number of top swimmers are (their friendly doctors say) asthmatic, why so many archers have heart conditions requiring beta-blockers (steadies heart rate and thus aim), and so on.
Now, as a cismale gets older, his testosterone may decline, leading to loss of bone and muscle mass, depression, disturbed sleep, loss of libido and so on. If I go to the doc reporting these symptoms (as a 48yo cismale) and get tested and my T is low, the doc will tell me to go away and eat better food, exercise, sleep right and so on, and come back in three months and get tested again. If it's still low then, they'll put me on TRT - testosterone replacement therapy. In Australia, this is a dose of 4 or 8mg a day (like nicotine patches), which is 28-56mg a week. By comparison, Arnie in the 1970s took 250mg a week, some of the huge powerlifters now are on 3-7,000mg a week. So we are talking about a person with a genuine medical need, and small supplementation.
There is no therapeutic use exemption for TRT. WADA and others say, "We have all respect and sympathy for your condition, but if you take that medicine, you cannot compete."
I believe it should be the same for transwomen with T above that allowed ciswomen. Excluding people from competition to ensure fairness is not in any way failing to respect them as human beings, or lacking sympathy for their person physical and mental health struggles. Saying, "transwomen should have under 5, too," is not oppressive of transwomen any more than "you can't do TRT and compete" is oppressive of elders. It's just about fair competition.
The alternative is, as I said, to allow ciswomen to juice up to 10nmol/dL, too. Personally I'm in favour of this. The most famous athletes who bring lots of money into the sport are never allowed to test positive, anyway, so it's mostly bullshit. But nobody's going to admit this, so we're left with the charade. If ciswomen have to play in the drug-testing charade, transwomen do, too. This may mean that very few transwomen get to compete. But I don't believe there's a human right to compete in sports. And nothing stops them competing in untested sports, anyway.
I'm not too concerned about MMA because everyone is juiced to all fuck and the drug-testing is even more comedic than that for Crossfit; ciswoman or transwoman, you're always going to get some hugely-muscled person pounding your head into the mat either way. I mean other sports where the testing is less obviously bullshit, like the 100m sprint or the Tour De France.
On-topic: a denial of the reality of the physiological differences between men and women is a key part of modern progressive ideology, just as a denial of climate change is a key part of modern conservative ideology. Both are wrong-headed, but as I said, the progressive denial of science is not as globally-damaging as the conservative denial of science, so it doesn't concern me as much.
This was not always so; the left has as bloody a history as the right, it's simply that the left has far less influence than it used to since the fall of the Soviet Union, and the english-speaking internet is dominated by US politics which overall swings right. But until the likely breakup of the United States, progressive ideology will remain marginalised in the West, and so will be less damaging than conservative ideology is.