Rolfe
Adult human female
What "lobby" did the IAAF and IOC "cave in" to when they made their original provisional decision to allow Semanya to compete in the women's category?
Oh and I never talked about "prohibition" or "power to prevent". FINA could, for example, arbitrarily impose a ban on all male swimmers over 5ft 10 in height if they wanted to. Nothing would stop them from doing so, and they'd have the power and authority to enforce such a ban in all events that they controlled. But of course they'd very soon a) find themselves up in court in multiple national and transnational (eg CAS) jurisdictions regarding the fairness and proportionality of such a ban, and b) severely tarnish their reputation for competence and evidence-based administration.
QED
I'm not sure whether they would find themselves in legal trouble were they to do anything so unlikely as banning swimmers over a certain height, but this is pretty academic. I am absolutely certain they would not have faced any successful challenge had they decided from the outset not to change the eligibility criteria for women's events. It has always been agreed that not allowing males to enter female events is both fair and proportional, and that could not have been successfully challenged. (I won't say "not challenged", because we all know the trans crybabies will challenge anything in the hope someone will take them seriously.)
You really need to get your head round the reality that "transwomen" are male and always will be, and that it is entirely legal, fair, proportionate and proper to treat them as male in appropriate circumstances, at least outwith wildly mad jurisdictions such as Canada and Australia.
Since sports are played by bodies, not gender identities, the big mistake that was made by FINA and others was caving in to the ludicrous proposition that gender identity is something they should pander to, rather than maintaining the sex-based categories as they had always been. Now they're having to unbake a cake they should never have put in the oven in the first place.