I can see what you're saying, but transphobic people are going to believe whatever they want to believe whether they've had any way to verify it or not. The idea behind why they're always yelling about chromosomes ties into that, as the vast majority of people will never a karyotype test in any way, but they're confident that they know what's happening inside of every person they see on a genetic level. I don't think we should be afraid of learning more about who we are and what makes us tick out of fear of how bigots will use it, as they will always find ways to hurt us. But, I can understand the concern at the same time. It's definitely something to keep in mind for the future.
It is not your choice what pronouns people identify with. They/them has been used for a long time as a singular pronoun in language and quite a few nonbinary people use it for themselves. Telling someone that you wish they were using a different pronoun than the one that they are is pretty insulting and it's why you're receiving a lot of backlash.