Some of the posts on here are hateful and transphobic (I'm not talking about the ones saying transwomen shouldn't compete against cis women BTW, but the ones who try to insist transwomen are not women).
For my take on the debate I do agree that certain transwomen competing against cis women is akin to a cis women taking steroids/testosterone competing against cis women not taking these which would be seen as an unfair advantage.
Saying that, a transwomen competing against cis men can be seen as unfair in the same way if they've taken hormone replacement for a while as their testosterone levels would be much lower than the average man.
I do like the idea someone mentioned of transwomen having had to take hormone replacement for long enough to decrease their testosterone to cis female levels before being allowed to compete against cis females.
I also like the idea of having your women's sports, men's sports, then a free for all everyone can compete just because that sounds like it could be fun.
Haven't gone through all twelve pages (partly due to some of the hate) but in case anyone hasn't mentioned it, aside from the gender identities male, female, non binary, gender fluid, and everything in between, just considering for once the purely physical sex rather than gender categories you can pass on x or y to your children.
Xy is male at birth. Xx female at birth. However you can also get combinations such as xxy and xyy. Xyy presents as male sex. Xxy again tends to present as male, but has different levels of testosterone and characteristics to Xy.
Then you get into intersex. A baby born with both male and female parts. This gets complex as there are various causes. You can have Xx intersex, Xy intersex with all kinds of causes. If you have an Xy baby for example who is unresponsive to testosterone so has even less than a cis woman and thus more female and less male build and other characteristics than cis women, would you consider them male or female when it comes to sports.
Added to that you can get xxx or even xo (only one x chromosome).
I think op's question could make an interesting debate if we don't devolve into transphobia (including deliberately misinterpreting what trans is. I've seen a few posters who've phrased it as a flippant choice) and I greatly thank those of you who are considering the subject objectively and not filling this thread with more hate.
P.s. For the poster who stated transwomen were not women as they can't bear children, please think things through before posting. There are plenty of cis women who are also unable to bear children.