I haven't even read this article, but this is sort of a point I get. Now, we haven't done a DNA test on Caitlyn to see her chromosomes, but other than the fact she believes she's a woman, there's nothing objective we can point to that says she should or shouldn't be a woman. Her whole story strikes me as something that is personally subjective. Now that's all fine and dandy, but people have to start admitting that there isn't really any (as of yet) objective basis for race either. So if race is subjective, and gender is subjective (both are social constructs, right?) then why can't a person elect to change their race?
For example, if there were a procedure (and in the future, there very well may be) to change one's skin tone, what moral basis would we have to stop people when we allow people to change their sex and gender. We would have none.