You're right - it doesn't matter and that was a lazy and admittedly somewhat disingenuous line of reasoning to bring up on my part.
Trans women in women's sports actually is a fairly unique and special circumstance and I regret bringing it up. When I say I don't think it's particularly important, I don't mean that I don't think it matters whatsoever - I thought I made that clear but perhaps I've meandered around the point. I mean it's not particularly important because there are just such a tiny quantity of trans athletes in the world. Granted - we can say that this tiny proportion of trans athletes are having an outsized impact on the far larger proportion of biological women by a minority who could be said to be cheating. We could also say that the affected group when we expand it to everyone who cares about sport, and fairness in sport, is negatively affected by the affected sports, competitions, fanbases and the like suffering from the sport that is their passion being somewhat discredited by the obvious lack of fairness.
But all that said... the trans people who choose to compete in competitions knowing (or in denial about the fact) that they have an unfair biological advantage compared to their competitors do not represent all trans people. They are a tiny, tiny minority. And the backlash against the actions of this tiny tiny minority taking advantage of the apparently completely incompetent and ineffectual regulatory bodies which could quite easily put a stop to this ends up affecting all trans people who have nothing to do with the individuals involved in these sports, or the decisions that allowed those few individuals to compete in the first place, by adding fuel to the already worryingly fierce blaze of anti-trans sentiment in much of the supposedly civilized, otherwise quite tolerant, lower-case-liberal societies. Because of this actually I just don't even believe that it's incompetence or "wokeness" that's preventing any clear lines from being drawn about what type of woman can compete as a woman, I think it's a deliberate tactic to make trans people just another oppressed, disadvantaged scapegoat for other problems in society...
...Which is why I'm now very wary of expressing particularly strong opinions one way of the other about whether trans women should be able to compete alongside biological women in professional sports. But fuck it I'll say it, most of the time they shouldn't. I still think it should be a case by case basis, ie, if male puberty was avoided, whatever other biomarkers can be objectively assessed and it can be demonstrated there's no remaining "masculine advantage", then I don't see any problem since there's no longer an unfair advantage. But most of the time, currently, in today's world, women's sports should be restricted to people who have been born women.
The changing room thing though... ugh, that I just cannot currently get past. I think it's a problem that only really exists because of the deeply repressed, puritanical, religiously-reinforced culture of shame around sex and gender and atypical sexualities and forms of gender expression. Dangerous, violent men can already enter women's changing rooms and threaten women. If a female-presenting "biological man" transwoman enters a woman's changing room just to get changed discreetly, I'm just not seeing an inherent danger here without getting back to the tired old trope that dangerous men might pretend to be trans women in order to access women's spaces and do bad things. I'm pretty sure the actual statistics on this do not support that hypothesis but someone correct me if I'm wrong.