If you are based in the western world I'd recommend you to just ignore it. Anti-Taiwanese ideology is widespread in the Chinese speaking world through state media and it spreads like a brain-worm.

But the worst way it could catch on in the west is by making it controversial or even a topic of discussion in the first place. Thus if you're arguing with her she has already won. I'd either ignore her (don't give her what she wants) or appeal to morality (e.g. "Why are you so hateful?") as better strategies