This is what republicans have always done well. They organize locally, take over school boards and city councils, drive the change they want to see in local communities and drive support locally to drive voter turn out nationally.
We don’t see democrats crashing school board and city council meetings, participating in local politics en mass to drive local change with near the same effectiveness as republicans, and it leads to underwhelming participation in national elections, as the left sits around wondering “what has the DNC done for me”.
Below the elite level, relative skill differences can be large enough that a skilled cis women can outcompete a lesser skilled cis men. And that’s where 99% of sports are played so these rules/laws just serve to make cis men not feel threatened by potentially losing in a softball game to a woman.
At the more elite levels, though, the skill gaps are much smaller, and being faster or stronger are the difference. Most WNBA players can’t dunk, most NBA players can. Elite men run 100M a full second faster than elite women. At those levels, men have a distinct physical advantage.
There have been some studies indicating trans women still have higher lung capacity than cis women, more strength etc, but there’s still some uncertainty because the number of studies are limited, and there’s even one study that indicated cis women may have an advantage over trans women.
But considering the laws currently being passed, they aren’t targeting elite athletes, and are instead targeting kids, and not out of the spirit of competition, but out of hate.