It's important to know WHICH sports people are expressing opinions on.
Not really, no. We have a wealth of statistics, spanning almost a century, for a wide range of sports. Everything from weightlifting to chess, there's a distinct gap.
ETA: And as I said below, if you're not talking about all sports, there's no reason to talk about which specific sports. If transwomen compete as males in some sports, why shouldn't they compete as males in all sports?
I feel sorry for trans women who are barred from competing in Athletics because there isn't a category for them at events.
They do have a category: the open category, which is dominated by males like themselves, for reasons which have been well established by now.
I don't think they should compete against women (I'm a runner, and I know that men are almost always faster than women due to muscle composition, heart and lung size, etc), but I don't know what the solution is.
Males compete with other males, not with females, is what the solution is.
Some sports may find men and women more comparable in performance but I haven't researched anything other than running.
All you have to do is look up the stats, going back decades, for any contest that measures weight moved, distance thrown, or speed traveled. That won't cover combat sports or sports that are judged subjectively, but it should provide you a wealth of insight into the real extent of the difference.
Actually, it there are sports in which trans women can fairly compete against cis women, distance running would likely be one of them. Biological men on the average have more hemoglobin in their blood than biological women do, meaning that they can transport more oxygen to the muscles that need it, but, according to the articles that I've seen, it takes only a few months of hormone therapy to reduce the hemoglobin level to that which is characteristic of biological women (on the other hand, muscle mass does not reduce nearly as rapidly).
You could look up the men's and women's distance running records over the years.
And also, why would it even be necessary, to make this one exception? Even if a transwoman could theoretically not enjoy an unfair advantage in this one particular sport, why shouldn't they just compete in the open/male category, same as they do in every other sport?
If the point is to validate a transwoman's perception of being a woman, letting them compete with women in one sport but not any of the others won't do at all. On the other hand, if that isn't the point, then transcending sex segregation in any sport is unnecessary. (And it follows from this conclusion that it's not necessary for transwomen to transcend sex segregation of any kind that society currently considers beneficial or necessary to women.)