I can't believe it took the bigots this long to get to the chromosome argument. The irony of this argument is that most doctors don't even know why it's bunk.
The chromosome myth was started when genetic testing was first made possible, they used a small sample population. The findings were that almost all the male homo sapiens of the test possessed the chromosome now labeled as Y, while most of the females possessed two of the chromosomes called X.
The fact is, we knew almost nothing about mutations, and genetics, when this was published. As per the standard routine, the media reported it incorrectly and the myth took off.
Without a resource like the internet, the game of telephone took off and eventually this myth was even taught in schools as fact. No one questioned it, why would they?
Less than 10% of homo sapiens go through genetic testing, even today. We also have not fully mapped the human genome, mapping means we have an understanding of how genes interact, genes do not do things on their own, they create chemicals based on other genes being present.
Which, ultimately, explains why there are many males born with female anatomy but male hormones, females born with testicles instead of ovaries, and why the binary gender system is so rare in nature. Hint: our genders are not binary, but the system is now broken so only one set can reproduce.
The most successful species have no gender, of very fluid gender reproduction, like frogs able to change their genders based on need. Ultimately, we now see that nature rarely selects a rigid reproductive system, thus, our entire concept of male and female is wrong.
So when you attack transgendered folks based on chromosomes you are, in fact, informing the world that you are an uneducated troglodyte incapable of learning.