It is a very difficult subject to discuss civilly, so I try hard—I don't want to offend anyone and know some people on both sides will be offended no matter how politely we try to talk.
I thank you for your link, but I must note that even that study found differences. For example: "Transgender women athletes demonstrated higher absolute handgrip strength than cisgender women, with no difference found relative to fat-free mass or hand size." Whatever anyone thinks the Y chromosome may be, it has some effect, which may explain why XY competitors tend to do very well in women's sports, while few XX competitors excel in men's sports.
I'll repeat that I fully support people's right to choose their gender and live socially as they please. I think we need to find a way to deal with cases where sex rather than gender appears to make a difference, and I hope we find that way soon.