Just going to leave a comment here because it's the highest up comment chain where you're cherry picking a single scientific article and ignoring the complexity of the problem. There's a few issues with what you're doing and I don't really have time to write up an entire guide as to why this isn't nice, but I'm just going to leave the following points:

• This is the LGBTQ+ community, please chill with the antagonism. If you want to make a point about whether testosterone provides an advantage to individuals, you're welcome to do so, however it needs to be done with caution if you're not a medical professional capable of examining a complicated question and exert good faith to fully investigate the issue at hand.
• To articulate this point, a cursory google of the issue at hand here 'trans women in sports' revealed the following 4 top results from vaguely reputable/scientific resources: 1 2 3 4. All four of these articles touch on a lot more than just testosterone levels contributing to performance in sports.
• A cursory review of the regulating bodies themselves would reveal poor control over who is allowed to compete. There's no discussion about this present in your point.
• A cursory review of the effects of testosterone on performance in athletes would might reveal any of the following studies: 1 2 3 4. The idea that testosterone is correlated with a positive performance from male athletes is a simplistic and flawed one. Young boys pre-puberty outperform young girls showing a more complicated story than just testosterone and pointing us towards more likely important factors, such as the social and environmental ones. Additionally, while testosterone may contribute to performance in some sports, it definitively does not for certain sports (especially since we're in a topic about chess). Reducing a complicated topic to a single dimension generally doesn't work and isn't a good basis for argument.
• With all that being said, you're right that for some trans women their testosterone levels may not be fully suppressed with just estrogen treatment, but nearly no regulatory bodies care about that - they care about whether the testosterone levels that they test are above a certain threshold. If they are not, they aren't allowed to compete. It's ridiculous to be quoting this study at all, because if someone were at that level and wanting to compete they'd have to be on testosterone blockers or post-op so as to drop their levels to an acceptable range.
• I cannot stress enough how bad it looks for someone to be coming in here and challenging the people directly effected by this issue with such a one-sided and shallow point. In general if you're going to come in and challenge a minority on something, you need to be extremely cautious about how you do so. Ask yourself, are you an expert on the topic? If not, what could you be missing? Should you seek out education before providing your opinion and attempting to provide "scientific" reasoning for your stance? Ask yourself whether others have likely shared the same opinion as you are sharing- are you bringing anything new or useful to the table? Might minorities already be inundated with people sharing the same opinion, in a scientific manner or not, and might you be contributing to their emotional and educational burdens?

In pre-op trans women. In post-op trans women the testosterone drops to zero ... the IOC requires women to be post-op in order to compete, for example.

So your "actual scientific fact" is a nicely cherry-picked piece of BS.

Yeah, that's like, one example. Trans women aren't exactly setting the athletic world on fire.