The problem is that there's a linguistic bait-and-switch going on.
If you use the more historically common usage of "man" and "woman" to be directly tied to "male" and "female", and that "gentlemen" and "ladies" to refer to these, respectively, then nobody is excluded.
The issue is that we're being asked to change those terms, and that's what creates the inclusion issue. So the purported solution to another problem is creating this issue. So, see, it's not a matter of evidence. It depends on how you want to define your terms. It's after you define your terms that you can look at the evidence and tell what fits where.
This whole kerfuffle is a series of definitional changes creating a cascade of issues that are solved by further definitional changes. But the truth is, there was no issue with the original definitions. You could easily have included and supported trans people without changing the existing words.