I had this conversation with my mom recently, who's a lib but also a 50 year old upper middle class white woman so it's not surprising she picked up some brain worms.

Basically, her entire viewpoint revolved around her ignorance of the fact that T blockers exist. Once I explained that to her, and talked about the studies of trans military members (which are some of the best info on how exactly transitioning effects athletic performance we have) which show that trans women's performance becomes comparable to cis women's after about a year of hormones, she admitted that she really didn't know anything about the issue beyond her knee-jerk reaction and conceded that I was probably right.

Now if you're arguing someone who you don't have a good enough rapport with that they can admit they were wrong, they won't do it. But that doesn't mean you can't get the ideas in their head and maybe when they're having a self-reflective moment they'll remember them and realize they were wrong retroactively.