Just a personal anecdote. I have intense emotions when dealing with transphobia but I think I'm able to think clearly. I think there absolutely are times where intense emotions can cloud thoughts but I beleive the converse isn't true.
"Intense emotions can interfere with clear thinking" does not imply that "clear thinking is impossible when there are intense emotions"
The thing that really sucks is that tran women are gonna get absolutely dominated by cis men. HRT for long enough really does so so much to the body (hence why most sports allow trans people who have transitioned to compete). Tho trans men also would have insane advantage overs cis women if they competed together
Maybe there isn't any good solution. But what you are saying leads to a conclusion that there is no place in sports for trans people. Then again, these conversations always fall apart when we talk about cis people with abnormal hormone profiles.
End of the day, a lot of competitive sports come down to genetics. There isn't much room for someone with disadvantagious genetics to become the best in the world. For me, I don't see much difference in a trans woman who's transitioned being world class in swimming and a tall ass cis woman dominating in basketball. Especially when we don't see trans people sweeping in competitions as a wider trend