So when you say it's reasonable to ban those who've gone through a male puberty... but you do NOT mean banning males... then which of those approaches of permanent damage and medicalization do you favor in order to allow some males to compete against females?
I see that Mumblethrax already replied to you on this point. But I think I'll respond as well.
People who have had puberty blockers exist. Given current treatment trends, there will be more of them. Arguing against the treatment does not make these people go away in the near term. Therefore, it is quite feasible to have a stance on if and how to accommodate them in a variety of situations independent of any stance or debate on the appropriateness of the care that got them there.
I don't like using this analogy, but I think it's one that might be illustrative. One can be critical of reckless behavior that leads to contracting an easily preventable disease without being against treatment for the disease.
In other words, the opinion that they should not have had a particular treatment does not lead to a conclusion as to what you allow them to do post-treatment. Particularly when we are talking about treatment that happens as kids. It smells of punishing the kids because you don't agree with the decisions of the parents.
So I would suggest separating the arguments regarding the merits of a treatment plan from decisions about how to handle people who have had that treatment.
Additionally, you phrase this as if boys are put on puberty blockers for the purpose of competing in women's divisions in the future. That seems...odd, but I agree that regardless of the merits of any other reason for puberty blockers, that one would be ridiculously out of line. But I doubt it is happening. I can't see a whole lot of parents going:
"Hey, little Johnny, I'd like you to play baseball, but you suck. So we're going to turn you into a girl. Then you can play softball. By the way, your new name is Hilda."
Do you think this actual conversation or thought process goes on? Or do you think that twelve year old boys are likely to think:
"I like swimming, but I'm slow. So I'll tell mom and dad I'm a girl so they can put me on drugs and get me on the girl's team. Then I can WIN!!!"
There may be (a few) cases where a male transitions with the express intent to pursue a sports career as a woman. I'm not aware of any, but it's conceivable. (People are strange.) But that would most likely happen with adults (18+). Most of the cases you hear of in high school are, I think, kids who transitioned and
then figured out they liked or might be good at sports. (And in most of the cases I've seen, they shouldn't be on the girls' team, in my opinion.)
Ascribing sports competition as an actual motive for puberty suppression seems off base.
For those who go through puberty suppression and then discover sports, evaluate them as individuals.