They said all they find is one (dodgy) study saying there is no difference when men living as women compete against women.
First you have to define "living as a woman". A lot of (US, at least) sports organisations are just making that "tick a box on the entry form".
In which case there's a lack of specific evidence about "men who tick the F box" having an advantage in the same way as there's lack of evidence that "men who are called Keith" have an advantage...
But we don't let Keiths in if anyone points that out - we assume they perform the same as other men, and wait for someone to demonstrate that Keiths are different.
Salami-slicing a category, such as "men", and claiming that we suddenly know nothing about a subset is daft. Useful, for those trying to defeat rules, but daft.
"Scientific" studies would only start to make sense when you're actually talking about very specific measures, such as hormone treatment, but then you're into a whole world of philosophical issues. The fact that you can hobble someone from a higher category doesn't mean the end result is meaningful - you're comparing peak performers in one class against impaired performers from another class.
Anyway, rather than go straight into particular "studies", I think you might do better to look at other reviews first, and then go into studies from there, because you do need to focus on the "sport" as well as the "science". (Even if you could "equalise" male performance to female doesn't mean you should).
The World Rugby stuff was good. Some links:
https://www.mumsnet.com/talk/womens_rights/4096492-Excellent-podcast-on-the-process-for-developing-World-Rugby-s-transgender-policy
https://www.world.rugby/the-game/player-welfare/conferences/transgender