... and probably vice versa.
Nah, no reason to restrict historically men's sports leagues. These leagues are for the best of the best and if a woman can compete she should be allowed to. There are other leagues that have restrictions to help make sure certain groups that might otherwise be unable to compete for biological reasons (e.g. seniors, juniors, women, people with disabilities). I don't see anything wrong with that.
Drawing the line to ensure fair competition for those subgroups is often difficult given that the line is often blurry. That's certainly true for events like the paralympics. But they find a way to be inclusive but also as "fair" as possible. The same can be true for women's sports to be able to allow transgender women to compete but maintain the spirit of the separate league for women.
I didn't watch Jake's videos (his videos don't have a great track record of saying something interesting) so I'm not sure what the original point was, but how to handle transgender women wanting to compete in women's sports is a legitimate question in my opinion. I'd just say that the idea that allowing transgender women to compete in women's leagues will somehow cause significant harm to the women currently trying to compete is pretty silly. Better to error on a fairly inclusive set of rules to allow all women to compete but do so in a reasonably fair (biologically speaking) way.