If only good empirical books on trans research weren't burned by the nazis at the start of their regime and trans literature/research weren't being banned in the U.S. by the GOP...

I have published work in academia so I know from experience. Empirical evidence CAN be extremely biased depending on who is doing the writing. There's a reason there's a million (exaggerated, obviously I hope) studies showing that games are both good and bad, studies showing red wine both causes and prevents cancer, studies showing that the Brontosaurus wasn't a real dinosaur but a misplacement of two different fossils, oh wait just kidding there was a new study that says it IS a real dinosaur. People are people, there's no perfect study. When studying humans and their behavior, we only have theory that is constantly being rewritten. We have something called cronbach's alpha that states that as long as data reaches 71% consistency or higher, it's a valid study. All to say, you can't always trust empirical evidence
Science already supports the idea of different genders. A basic college biology course could tell you that. Forget "there's only two genders" the "two sexes" thing is also a myth. Humans have two different kinds of sex chromosomes, x and y. We can have I BELIEVE up to 3 at a time? XX is typically associated with FEMALE and XY is typically associated with MALE unless of course you have de la Chapelle syndrome and your XX chromosomes make you develop a penis instead of a vagina. This is just one example of being intersex. Up to 2% of the population is intersex, 4 times more than the number of cops in the U.S.
Gender being a science doesn't mean boomers are open and willing to unpack their views of gender though. Unlearning things is painful, scientifically speaking. People HATE unlearning things. There's lots of studies on cogitative dissonance, if you want to go read your empirical references.