Don't let them get you down, I've seen the argument multiple times online, people are holding on to it like it is their anchor, and it really is all they have against us at this point. It is their go to, whenever they want to try to justify their bigotry, because they believe it is rooted in science. It is almost certain, that when I watch a video regarding transsexuals or read a news article, the chromosomes argument is brought up frequently.
It is easy to argue against though, chromosomes do not always define sex.
I think ultimately, the world is rapidly changing, a lot of these people are terrified of these changes, and grasp on to anything they think they can tear apart to bring back what they are used to. Gender being a foundation of their world view is not as black and white as they want it to be, and they are having a hard time coming to terms with that.
These people are not going to give up anytime soon, to them, the world is crumbling into utter chaos and they are driven by paranoia and fear. Any attempt I have made with reasoning with them, often goes down the rabbit hole of insanity, and it becomes apparent just how scared they really are. They will often argue against the terms homophobia or transphobia, because they claim they are not afraid of us, but that could not be further from the truth, what we represent terrifies them.
There is a big movement of them on youtube, but eventually I think it will fizzle out, as they slowly get used to their new surroundings, and realize it is not as bad as they used to perceive it. A lot of them are very paranoid, and prone to believing conspiracies. Whatever you do, don't get caught up in their current of fear, because it is very easy to get pulled away in it.