I didn't say that sporting advantage was the only reason for transition, rather that they're using their trans status to cheat.
To cheat means "to act dishonestly or unfairly in order to gain an advantage"; so either they're transitioning dishonestly in order to gain that advantage in sport... or they're not cheating. If they are trans and they participate in a sport under the rules of the governing body, that's not cheating. Even if you think it gives them an advantage. They are not the arbiters of what is fair, sport is.
Also the US has some nuts rules around highschool sport, but I don't think it's necessarily helpful to talk about trans people in the US when we're talking about trans people in the UK; or are we? I assumed we were because of the usual self-ID connections to this debate, and that being a UK legislative change.
Should they be read as female and treated as such by men after transistion, they mistake the misogyny they face for transphobia.
Undoubtedly trans people do face transphobia; you know, people having a visceral reaction to that which is different? Really prevalent through human history, very very common.
Even if people reacted to them entirely as women they would be aware and affected by the societal rejection of that which is "different" and "unnatural"; it's the kind of transphobia that would make a trans woman afraid of being outed in the first place!
So no, that fear of outing for fear of reprisals is not anybody mistaking misogyny for transphobia. Jeez, can't trans people even name their own inequity now?