If that "gotcha" is true then having mens and womens facilities at all is equally equivalent to racism and we shouldn't have any division because its insulting to all men to be treated as if their presence creates an elevated risk for women - after all, the vast majority of men are nonviolent, honourable and no threat to women. But we know that some are not - the violent, the creepy, the predators - they exist and are a real threat.
There is no point at all having a division between mens and womens facilities that any male who wishes to is allowed into the womens side and no one is allowed to complain. It doesn't matter if the majority of males who benefit from that are nonviolent and no threat. It is 100% guaranteed that the creepy predators will and do take advantage of having carte blanche to ignore anything that suggests no men beyond this point if culture says that simply the words "but I'm not a man" have to be believed.
Don't forget that it's also transphobic to have any kind of barriers or standards in terms of medication/testosterone, surgery, or clothing, for a transwoman to qualify as a woman under the TWAW. An unmedicated TW with no surgery is just as much allowed to wear jeans and a t-shirt as any woman is.
It's muddled and irrational thinking without a coherent set of statements that hold it together. I've seen the memes being disparaging and sarcastic about "oh yes of course I've undergone years of therapy and difficult expensive treatment in order to (whatever)" but that conveniently ignores that the same ideological framework upholds that no therapies or treatments are required and a TW who doesn't have a hope of "passing" shouldn't be treated any differently from one who has made great efforts towards passing.
Your relative doesn't understand that admitting transwomen is legally and practically the same as admitting any male of any gender identity who wants to come in, and that will include some very dangerous ones. They are dismissing this because deep down they believe that the status of "woman" is so ignominious and shamefully low in the hierarchy of humanity that no male would ever claim it with any kind of ulterior motive, because the shame and debasement required would be sufficient barrier to stop a dangerous man from claiming that status.