there is probably no good reason
PROBABLY? How do you know the odds that there exists a good reason for a fear that you have already labeled irrational and alarmist? Are you saying there may be a good reason for those fears, but no one has offered it? Or just that you haven't heard it yet? Why did you feel compelled to put "probably" in your rejection of those fears? Do you "probably" disagree with Rowling, but maybe you don't?
And then there's that awful word "triggered." Not everyone with a concern is "triggered." Rowling has looked at the situation and said that women are scared by people with penises in their private spaces. That fear may be unnecessary in many, many cases. But it is not "irrational," and a person who observes that such fear exists is not "triggered" by anything.
Moreover, the fear is not that someone will be attacked by a man "identifying" as a woman, but by a man pretending to identify as a woman. It's hard to know the probabilities there until data is collected under the new rules. To say that a deterrent (in this case, barring penises from women's spaces) is unnecessary because it has been so effective finally gets us to an argument that is, indeed, irrational. I have had a burglar alarm on my home for many years and never been burglarized. Maybe I don't need the alarm....
Finally, the alternative to the woman with a penis using the women's room is using the men's room. Duh.