The distinction between sex and gender is not something they’re making up, and it is something to be taken seriously, within limits. Gender is something defined by culture, and gender involves roles that often – but not always – overlap with biological sex. There are some ancient cultures with three genders: three detailed ways that people were supposed to behave in the culture, in regards to patterns of sexual and non-sexual behavior.
So you’re not going to win an argument by saying that there ARE only two genders, since the word proves you wrong. Rather, the Catholic approach as I understand it is to say that human flourishing is promoted by people acting in accordance with their biological sex. We do not determine our sexual nature; it is given to us naturally. When people rebel against their sexual nature, it tends to lead toward suffering, not flourishing. Thus, even if there are however many genders, it would be best if there were only two.
It’s important to note, though, that simply forcing people into gender stereotypes is not the solution. The stronger and more exclusive our sexual stereotypes, the more incentive people have to rebel against them.
Also, it’s important to realize that there are genuinely intersex people. Catholics should not deny transgenderism in such an aggressive way as to alienate people who are genuinely confused about whether they were born male or female. Indeed, we should be open to research on this topic. If it turned out that some people have “brain sex” that is genuinely at odds with their body sex, I’m not sure what the right and loving approach would be.